If α,β are the zeros of a Quadratic polynomial such that α + β = 24, α - β = 8. Find a Quadratic polynomial having α and β as its zeros. (Ans: k(x^{2}- 24x + 128))
Ans: α+β = 24
α - β = 8
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2α = 32
α = 32/2 = 16, ∴ α = 16
Work the same way to α+β = 24
So, β = 8
Q.P is x^{2} - (sum) x + product
= x^{2} - (16+8) x + 16 x 8
Solve this,
it is k (x^{2} - 24x + 128)