Question

If α and β are the zeros of the quadratic polynomial such that α + β = 24 and α - β = 8, find a quadratic polynomial having α and β as its zeros.

Answer 1

A quadratic equation when sum and product of its zeros is given by:

f(x) = k{x² - (sum of zeros)x + product of the zeros},

where k is a constant

α + β = 24 ....(1)

α - β = 8 ....(2)

Adding 1 and 2 we get,

α + β + α - β = 24 + 8

⇒ 2α = 32

⇒ α = 16

Substitute value in 1 to get

16 + β = 24

⇒ β = 24 -16

⇒ β = 8

α = 16 and β = 8

f(x) = k{x² - (24)x + 16 × 8}

f(x) = k(x² - 24x + 128)

If we will put the different values of k,

we will find the different quadratic equations.