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

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]

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