Question

if alpha and beta are the zeros of the polynomial x square - 2 x minus 15 then form a quadratic polynomial whose zeros are 2 alpha and 2 Beta​

Answer 1

x2-2x-15=(x+3)(x-5)
Therefore the zeros of the polynomial are -3 and 5.
Therefore alpha= -3 and bita=5
2alpha=-6 and 2beta=10
Therefore a polynomial with the following zeros will be-
x2-(-6+10)+(-6)×10
=x2-4x-60

Ans:-x2-4x-60

Answer 2

given alpha and beta are zeroes of x^2 - 2x - 15

alpha + beta = -(-2)=2

2(alpha + beta) = 2*2= 4

2 alpha + 2 beta= 4

(alpha)(beta)= -15

4(alpha)(beta)= -15 * 4

(2 alpha)(2 beta)= -60

given  2 alpha and 2 beta are zeroes of another polynomial

the polynomial is = k( x^2 - ( sum of zeroes)x + (product of zeroes))

                       = k( x^2 - (2 alpha + 2 beta)x + ((2 alpha)(2 beta)))

                      = k(x^2 - (4)x + (-60)

                      = k(x^2 - 4x - 60) where k is any real number