Question

If alpha and beta are the zeros of the polynomial 2x²-7x+6, form a quadratic polynomial whose zeroes are alpha+2 and beta+2

Answer 1

Answer:

x2−11x+30.

Explanation:

Let, the poly. be p(x)=2x2−7x+5.

Then, p(x)=0⇒2x2−7x+5=0.

∴2x2−5x−−−−−−−−−2x+5−−−−−−=0.

∴x(2x−5)−1(2x−5)=0.

∴(2x−5)(x−1)=0.

∴ The zeroes of p(x) are 52,and,1.

We select, α=52andβ=1.

Letting α0=2α+1,andβ0=2β+3, we have,

α0=2(52)+1=6,andβ0=2(1