Question

If α and β are the zeroes of a polynomial X2 -x-30, then form a quadratic Polynomial whose zeroes are 2-α and 2- β

Answer 1

Answer:

x^2 -2x-15

=x^2–5x + 3x - 15

=x(x-5) + 3(x-5)

= (x-5)(x+3)

This means x=5 or x =-3

Hence α=5, β=-3

And 2α=10, 2β= -6

Now desired polynomial can be expressed x^2 -(2α+2β)x + (2α)(2β)

= x^2–[10+(-6)]x + (10)(-6)

x^2 - 4x -60