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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.

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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

⇒ - \(\frac{6}{1}\) = - \(\frac{b}{a}\)

⇒ b = 6 & a = 1

Also, product of zeroes = c/a

⇒ - 4 = \(\frac{c}{a}\)

⇒ c = - 4

& a = 1

∴ the polynomial is f(x)= x2 +6x-4

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