Question

If alpha and bet are zeros of the polynomial 4x^2 -x -4, Find the quadratic polynomial whose zeros are 1/2xalpha and 1/2bet ?​

Answer 1

Step-by-step explanation:

alpha and beta are the zeroes of the polynomial

4x²-x-4.

So alpha+beta=-b/a=1/4

and alpha×beta=c/a=-4/4=-1

now 1/2alpha=(1/2)×4=2

and 1/2beta=(1/2)(-1)=-1/2

So the polynomial whose zeroes are 2and-1/2

is x²-(sum of the zeroes)x+(product of the zeroes)

=x²-(2-1/2)x+2×(-1/2)

=x²-3/2x-1

=2x²-3x-2.(Answer)