Obtain a quadratic polynomial with the following conditions:
The sum of zeros = —3; the product of zeros = —4

Question

Obtain a quadratic polynomial with the following conditions:The sum of zeros = —3; the product of zeros = —4

Philoid · Accepted Answer

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

Given, α + β = –3 ; αβ = –4

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

Thus, b = –3k, a = k

And αβ = = – . So, c = –4a = –4(k) = –4k

p(x) = ax² + bx + c

∴ p(x) = (k)x² + (–3k)x – 4k

∴ p(x) = k (x² – 3x– 4)