Obtain a quadratic polynomial with the following conditions:
The sum of zeros = 2; the product of zeros = —3

Question

Obtain a quadratic polynomial with the following conditions:The sum of zeros = 1/3; the product of zeros = 1/2

Philoid · Accepted Answer

Let α and β be the zeros of the polynomial p(x) = ax² + bx + c.

Given, α + β = ; αβ =

We know that α + β = – = . So, – = = k, say

Thus, b = –k, a = 3k

And αβ = = . So, c = =

p(x) = ax² + bx + c

∴ p(x) = (3k)x² + (–k)x +

∴ p(x) = k (3x² – x + )

∴ p(x) = (6x² – 2x + 3) [Taking common]

Obtain a quadratic polynomial with the following conditions:
The sum of zeros = 1/3; the product of zeros = 1/2