Question

Let alpha and beta be the zeroes of a quadratic polynomial 2x^2- 5x-6 then form a quadratic polynomial whose zeroes are alpha + beta and alpha x beta

Answer 1

Answer:

Step-by-step explanation:

Since α and β are zeros, then 2x2-5x-6=2(x-α)(x-β).

(x-α)(x-β)=x2-(5/2)x-3

By Vieta Theorem α+β=5/2, αβ=-6/2=-3. Therefore

(x-(α+β))(x-αβ)=(x-5/2)(x+3)= x2+(3-5/2)x-15/2=x2+(1/2)x-15/2

=(1/2)(x2+x-15)