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root 6 plus root 6 till infinity is equal to

If α and β are the zeros of the quadratic polynomial f(x) = x2 - px + q, prove that a2/b2 + b2/a2 = p4/q2 - 4p2/q + 2Given that

αandβare the zeroes of the quadratic polynomialf(x) =x^{2}–px+qIn the given solution how did (a^{2}+ b^{2})^{2}- 2a^{2}b^{2}/ a^{2}b^{2 }changed into [(a + b)^{2}- 2ab ]^{2 }- 2(ab)^{2}/ (ab)^{2}i didnt understand how -2a^{2}b^{2}/ a^{2}b^{2 }change to^{}- 2(ab)^{2}/ (ab)^{2 }bcoz a^{2}b^{2}and (ab)^{2}are two different things. I guess !!i m confused..plzz help...If alpha and beta are zeroes of the polynomial x

^{2}- 6x + a.Find the value of a if 3alpha + 2beta = 20What Is Formula For Alpha minus Beta

(α-β)?

If alpha and beta are the zeros of polynomial x

^{2 }- 5x + k such that alpha-beta=1. find the value of k ......

^{x}- 13.6^{x}+ 6.9^{x}= 0, then the value of x isIf the polynomial x

^{4}- 6x^{3}+ 16x^{2}- 25x + 10 is divided by another polynomial x^{2}- 2x + k, the remainder comes out to be x + a, find the values of k and a.If graph of a polynomial does not intersects the x-axis but intersectd y-axis in one point, then no. of zeroes of the polynomial is equal to

Find ' k ' so that ( x

^{2}+2x+k ) is a factor of ( 2x^{4}+ x^{3}- 14x^{2}+ 5x + 6 ). Also find all the zeroes of both the polynomials.How can we find the HCF and LCM of 448, 1008 and 168 by using fundamental theorem of arithmetic ? . . . .

If one zero of the quadratic polynomial f(x) = 4x

^{2}- 8kx - 9 is negative of the other, find the value of k.1. If one zero of the polynomial ( a

^{2}+ 9 ) x^{2}+ 13x +6a is a reciprocal of the other, find the values of a. Also find the polynomial..2. Factorise p(x) = x

^{3}- 3x^{2}- 9x - 5 .3. If a and b are the zeroes of the quadratic polynomial f (x) = x

^{2}- p(x+1) - c, show that (a+1) (b+1) = 1 - c .4. The polynomial ax

^{3}+ bx^{2}+ x -6 has (x+2) as a factor and leaves a remainder 4 when divided by (x-2). Find 'a' and 'b' .5. If the polynomial x

^{4}- 6x^{3}+ 16x^{2}- 25x +10 is divided by another polynomial x^{2}- 2x + k , the remainder comes out to be x+a . Find k and a .6. Find the zeroes of the polynomial f(x) = x

^{3}- 5x^{2}- 16x + 80 , if its two zeroes are equal in magnitude but opposite in sign.(A) 7

(B) 14

(C) 21

(D) 6

If two zeroes of the polynomial p(x) = x

^{4}- 6x^{3}-26x^{2}+138x -35 are 2+root 3, find the other zeroes.If alpha and beta are the zeroes of the polynomial f(x) = ax

^{2}+ bx + c, then evaluate1)alpha

^{2}+ beta^{2}2)alpha/beta + beta/alpha

3)alpha

^{3}+ beta^{3}4)1/alpha

^{3}+ 1/beta^{3}5)alpha

^{2}/beta + beta^{2}/alphaplease help mee...

expert again don't post the similar question link the one u posted earlier was not at all the answer :(

^{2 }+ bx + c and a+b+c=0 then one of the zero(i) -b/a (ii) c/a (iii) b/c (iv) none of these

If alpha and beta are the zeroes of the quadratic polynomial f(x) = x

^{2}- px + q, prove that alpha^{2}/beta^{2}+ beta^{2}/alpha^{2}= p^{4}/q^{2}- 4p^{2}/q + 2.a quadratic polynomial px

^{2}+qx+r has zeroes a &b . find the polynomial whose zeroes are 1/a & 1/b.Find all the zeros of 2x

^{4}-9x^{3}+5x^{2}+3x-1 if two its zeros are 2+ root 3, 2- root 3 pls answer with explanation^{(x)}=x^{4}+2x^{3}-2x^{2}+x-1 so that the resulting polynomial is excatly divisible by x^{2}+2x-3?^{2}-7.^{3}+x^{2}-6x-3, if 2 of its zero's are minus root 3 and root 3.^{2}=5x=6 and verify the relationship between the zero's and the co-efficient.^{2}-2x-8,then form a quadratic polynomial whose zero's are 2alphaand 2beta.If alpha and beta are the zeroes of the polynomial 21y

^{2}-y-2, find a quadratic polynomial whose zeroes are 2alpha and 2beta.Formulae for alpha square plus beta square

maximum how many number of zeros can a biquadratic polynomial have?

Given that root 2 is a zero of the cubic polynomial 6x3 + root2 x2 – 10x – 4 root2 , find

Given a

^{2}+ b^{2}= 1, c^{2}+ d^{2}= 1, p^{2}+ q^{2}= 1, where all numbers are real , thenIf alpha and beta are zeros of a polynomial ax

^{2}+bx+c then evaluate alpha-beta.Find the third zero of the polynomial, if the sum and product of whose zeroes are -3 and 2.

If alpha and beta are zeros of quadratic polynomial f(x)=x

^{2}-2x+3 find polynomial whose roots are alpha+2,Beta+2^{2}+kx+k ,k not equal to 0 cannot both be positive. Explain the statement.How can you prove it?If alpha and beta are the zeros of quadratic polynomal 2x2-5x+7 , find a polynomial whose zeros are 3alpha+2beta and 2alpha+3beta

to draw the graph of a quadratic polynomial and observe

(i) the shape of the curve when the co-efficient ofx square is positive and (ii) same when its negative

If the polynomial 6x4 + 8x3 + 17x2 + 21x + 7 is divided by another polynomial 3x2 + 4x + 1, the remainder comes out to be (ax + b), find a and b.

^{2}- 8x - 6 and verify the relationship between zeroes and coefficients of the polynomial.Given that x – root 5 is a factor of the cubic polynomial x3 – 3 root5x2 + 13x – 3 root5 ,

The number of positive integral solution of 2x + 3y = 763 is

1) 125

2) 126

3) 127

4) 128

Plz answer with explanation !!

If p(x) = ax

^{2}+ bx + c, then c/a is equal toIf sum of the square of zeros of the quadratic polynomial f(x)=x^{2}-8x+k is 40 find the value of KReply it fast..

find the value of k for which the p(x)=x

^{4}+10x^{3}+25x^{2}+15x+k is exactly divisible by x+7. how to solve it?If the zeroes of the polynomial x3 - 3x2 + x + 1 are a-b, a, a+b, then find 'a' and 'b'.

If alpha and beta are zeroes of polynomial 3x

^{2}+ 2x - 6 find the value of alpha-beta, alpha^{2}+ beta^{2}, alpha^{3}+ beta^{3}, and 1/alpha + 1/beta.If (x-k) is a factor of the polynomials x

^{2}+ px + q and x^{2}+ mx + n, Prove that k = (n-q) / (m-p)Find the zeroes of the polynomial

4t^{2}- 5.if d is the HCF of 45&27,find x,y satisfying d=27x+45y.

For each of the following, find a quadratic polynomial whose sum and product

If the squared difference of the zeros of the quadratic polynomial f(x) = x^{2}+px + 45 is equal to 144, find the value of p.if the product of two of the zeroes of the polynomial 2x

^{3}-9x^{2}+13x-6 is 2, the third zero of the polynomial is :-if the zeroes of the polynomial x

^{2}+ px + q are double in value to the zeroes of 2x^{2}- 5x - 3 ,then find the value of p and qIf 1 is zero of the polynomial p(x) = ax

^{2}- 3(a-1)x - 1, then the value of 'a' is^{2}- 2x - (root 5) find the value of (alpha^{2}-beta^{2}) - (alpha-beta)^{2}- (alpha+beta)^{2}where alpha and beta are zeroes of the polynomial.What must be subtracted from the polynomial f(x) = x

^{4}+ 2x^{3}- 13x^{2}- 12x + 21 so that the resulting polynomial is exactly divisible by x^{2}- 4x + 3 ?pls do it urgently

ppt project on polynomials

If a and b are zeroes of the polynomial x

^{2}- x - 6, then find a quadratic polynomial whose zeroes are (3a + 2b) and (2a + 3b)?Pls give the answer as soon as possible...

If one zero of a polynomial 3x

^{2}-8x+2k+1 is seven times the other. Find the value of kx^{2 }+ 11x^{4 }+ β^{4}(ii) $\frac{1}{\mathrm{\alpha}}+\frac{1}{\mathrm{\beta}}+2\mathrm{\alpha \beta}$.pl. provide the answers

if

αandβare the zeros of the quadratic polynomial f(x) =ax^{2 }+bx+c, then evaluate:(i)α-β(ii)=1/aα +b +1/aβ+b(iii)β/aα +b +α/aβ+ba quadratic polynomial can have how many zeros?

A. at most 2 zeros

B. at least 2 zeros

C. only 1 zero

D. exactly 2 zeros

Obtain all the zeroes of the polynomial f(x)= 2x

^{4}-2x^{3}-7x^{2}+3x+6, if its two zeroes are√3/2 and -√3/2find the zeroes of the cubic polynomial:

2x

^{3}-5x^{2}-14x+8?Verify the relationship between the zeroes and coefficient.

Find the zeroes of p(x) =3x

root^{2}+ 10x + 73 & the relation between the zeroes and coefficient of the polynomial.root1) if a and b are the zeroes of the quadratic polynomial f(x)= x2-5x=4, find the value of 1/a+1/b+2ab.

2)find the zeroes of the quadratic polynomial 4root3x2+5x-2root3 and verify their relationship.

3)find all the integral zeroes of x3-3x2-2x+6

4) if (x-2) and (x-1/2) are the factors of the polynomials qx2+5x+r then prove that q=r

if alpha and beta are the zeros of polynomial f(x) = x

^{2_}5x+k such that alpha--beta = 1, then find kis polynomial y

^{4}+ 4y^{2}+ 5 have zeroes or not ?If the polynomial 6x

^{4}+ 8x^{3}- 5x^{2}+ ax + +b is exactly divisible by the polynomial 2x^{2}- 5 , then find the value of a & bpls do it urgently

Find the largest number which divides 71 and 126, leaving remainders 6 and 9 respectively.if alpha and beta are zeroes of 2x^2+5x+k, satisfying alpha^2 + beta^2 +alpha beta=(21/4), find k

If ( x + 1 ) is factor of f(x) = a

_{0}x^{n}+ a_{1}x^{n-1}....... + a_{n}= 0, then_{0}+ a_{1}..... a_{n}= 0_{0}+ a_{2}+ ...... = 0_{1}+ a_{3}.......... = 0_{0}+ a_{2}+ a_{4}..... = a_{1}+ a_{3}+ a_{5}......check whether 15^n can end with digit zero for any natural number n

Find the zeroes of the polynomial 2x2+px-p2.

If the polynomial f(x) = ax

^{3}+ bx - c is divisible by the polynomial g(x) = x^{2}+bx+c, then ab =a) 1 b) 1/c c) -1 d) -1/c

also, in the above question c =

a) b b) 2b c)2b

^{2}d) -2ba) b b) 2b c) 2b2 d) -2b

DIVIDE 3X^{5}- 2X^{4 }+X^{2}- 2 BY X^{2}+ X+ 1 AND VERIFY THE DIVISION ALGORITHMIf alpha beta are roots of the polynomial f(x) = x

^{2}-px+q then Find value of1) alpha

^{2}+ beta^{2}2) 1/alpha + 1/beta

3) alpha/beta + beta/alpha

Obtain all the zeroes of x

^{4}-7x^{3}+ 17x^{2}- 17x + 6, if two of its zeroes are 3 and 1 ....??If the remainder on division of x3 +2x2+kx+3 by x-3 is 21, find the quotient and the value of k.Hence find the zeros of the polynomial x3+2x2+kx-18

-3/2root5 , -1/2

if m and n are zeroes of the polynomial 3x

^{2}+11x-4.find the value of m/n +n/m^{4}−9𝑥^{2}+9 by the polynomial 𝑥^{2}−3𝑥 and verify the division algorithm.I am not understand this answer given in the meritnation. please explain

show that one and only out of n , n+2 , n+4 is divisible by 3. where n is a positive integer

if α, β are the roots of the quadratic polynomial p(x) = x

^{2}-(k-6)x+2(2k-1).Find the value of k,ifα+β = 1/2αβ.Find a quadratic polynomial whose zeroes are 3+root 5 & 3-root5

ANSWER ASAP

if alfa and beta are the zeroes of of quadratic polynomial f(x)=x

^{2}-3x-2'find quadratic polynomial whose zeroes are 1/2alfa+beta and 1/2beta+alfaa) both negative b) one positive one negative

c) both positive d) both equal

explain the ans with solution plzzzzzzzzzzz

1)if alpha and beta are the zeros of the polynomial x2 -6x +k,what is the value of k when 3 alpha + 2 beta =20

2)if alpha and beta are the zeros of the polynomial 2x2 +7x -3, then the value of 1/alpha +1/beta

3)the quadratic polynomial p(x) with -81 and 3 as product and one of the zeros respectively.what is the polynomial

4)if x+1 is a factor of 2x3 +ax2+2bx +1 find the values of a and b where 2a-3b=4

5)if one solution of the equation 3x2-8x+3k+1 is seven times the other find the soultions and the valure of k

6)if one zero of the polynomial(a2+4)x2 +13x +4a is the reciprocal of the other,find the value of 'a'

(7)if alpha and beta are the zeroes of the quadratic polynomial x2-(k+6)x + 2(2k-1),find k such that alpha + beta =1/2alphabeta

(8)find the values of a and b such that x4+x3+8x2+ax+b is divisible by x2+1

(9)when the polynomial 4x4-5x3-39x2-40x-2 wadivided by the polynomial g(x) the quotient and the remainder were x2-3x-5 and -3x+8 respectively.Find g(x).

find the zeroes of quadratic polynomial 4 root 3x square + 5x - 2 root 3 and verify th relationship between the zeroes and its coefficients

Find the square root of 10+√( 24)+√( 60)+√40

Angle between the minute hand of a clock and hour hand when the time is 7 : 20 am is :

$Q.P\left(x\right)={x}^{2}+2\sqrt{2}x-6$

Find the zeroes of the quadratic polynomial 6x

^{2}- 7x - 3 and verify the relationship between the zeroes and the coefficients.form a quadratic polynomial whose one zero is -15 and the sum of the zeros is 42