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