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) .

1) Here is the link for the answer to a similar query:

 

https://www.meritnation.com/ask-answer/question/if-alpha-and-beta-are-the-roots-of-x2-5x-a-0-and-2alpha-5b/quadratic-equations/3162043

 

2) Here is the link for the answer to a similar query:

https://www.meritnation.com/ask-answer/question/if-alpha-and-beta-are-the-zeroes-of-x2-7x-12-then-find-the/math/4948188

 

Due to paucity of time it would not be possible for us to provide the answers to all your queries. We are providing solutions to some your good queries. Try solving rest of the questions yourself and if you face any difficulty then do get back to us.

  • -2

  It is not possible to answer these ques. in one time. Therfore i can give u hints or way to solve..

1)Here, alpha + beta = -b/a  =  6  &  alpha *beta = c/a = k

given,3alpha+2beta = 20  ..  now square on both side & put the values of alha + beta and alpha * beta

then, u get your required result..

2) alpha +beta = -b/a = -7/2 & alpha*beta = c/a = -3/2

now, 1/alpha + /beta = alpha + beta/ alpha *beta

  = -7/2  = 7/3

  -3/2

3) let alpha =3 & alpha * beta = -81

therefore, beta = -81/3 = -27

hence, required polynomial = k[x2- [alpha +beta] + [alpha+beta]       =k{x2-[-27-3]x +[-81]}

  = k [ x2+30x - 81]

  • -7

if x+1 is a factor then x=-1 is a zero

therefore, p[ -1 ] = 2[ -1]3+a[ -1]2+2b[ -1] +1

  0 = -2+a -2b+1

  1 = a-2b  .................A

given,2a -3b = 4  ..................B

Now, solve a&b by elimination method,which is required answer.

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Rest of the questions are similar, try to do them.If u have any problem see R.D. Sharma textbook.

I HOPE, NOW YOU WILL HAVE NO PROBLEM....

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