1. If one zero of the polynomial ( a2 + 9 ) x2 + 13x +6a is a reciprocal of the other, find the values of a. Also find the polynomial..
2. Factorise p(x) = x3 - 3x2 - 9x - 5 .
3. If a and b are the zeroes of the quadratic polynomial f (x) = x2 - p(x+1) - c, show that (a+1) (b+1) = 1 - c .
4. The polynomial ax3 + bx2 + 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 x4 - 6x3 + 16x2 - 25x +10 is divided by another polynomial x2 - 2x + k , the remainder comes out to be x+a . Find k and a .
6. Find the zeroes of the polynomial f(x) = x3 - 5x2 - 16x + 80 , if its two zeroes are equal in magnitude but opposite in sign.
the given polynomial be
if one zero is the reciprocal of the other.
product of the zeroes = 1.
thus a-3 =0 i.e. a =3
thus the value of a is 3.
at x = -1
therefore by the factor theorem : is a factor of p(x).
now dividing p(x) by (x+1)
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