Question

If alpha and beta are the zeroes of x2+5x-7 then frame a polynomial whose zeroes are 2alpha and 2beta

Answer 1

If α and β are zeros of a polynomial,
ρ(x) = x^2 - (α + β)x + αβ

So given polynomial has,
α + β = -5
αβ = -7

So, polynomial with zeros as 2α and 2β will have

Sum of zeros
=> 2α + 2β
=> 2(α + β) = 2x(-5) = -10

Product of zeros
=> (2α)x(2β)
=> 4αβ = -28

Therefore the new polynomial will be:
ρ(x) = x^2 - (2α + 2β)x + 4αβ
= x^2 + 10x - 28