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

Question

Polynomials

Answer 1

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)

Answer 2

2x² - 5x - 6 = 0

The roots are irrational. Therefore A and B are irrational.

A + B is irrational and A*B is irrational

This whole problem is irrational!