If α, β are the zeros of a polynomial such that α + β = – 6 and αβ = – 4, then write the polynomial.

Question

Philoid · Accepted Answer

For any polynomial, f(x) = ax² + bx + c

The sum of zeroes, is given as -b/a

& the product of zeroes is given as c/a

Here, the sum of zeroes is given as -6 = -6/1

⇒

⇒ b = 6 & a = 1

Also, product of zeroes = c/a

⇒

⇒ c = -4

& a = 1

∴ the polynomial is f(x)= x² +6x-4