If α and β are the zeros of the quadratic polynomial such that α +

1.	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» 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.

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»

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.