Q. 4 C5.0( 2 Votes )

# Obtain a quadratic polynomial with the following conditions:

The sum of zeros = 1/3; the product of zeros = 1/2

Answer :

Let α and β be the zeros of the polynomial p(x) = ax^{2} + 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) = ax^{2} + bx + c

∴ p(x) = (3k)x^{2} + (–k)x +

∴ p(x) = k (3x^{2} – x + )

∴ p(x) = (6x^{2} – 2x + 3) [Taking common]

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