Q31 of 109 Page 3

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


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