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Mathematics

Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.

14,−1\dfrac{1}{4}, -1

Polynomials

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Answer

For given roots,

Quadratic equation : x2 - (Sum of roots)x + (Product of roots) = 0

Substituting values we get :

⇒x2−14x+(−1)=0⇒x2−14x−1=0⇒4x2−x−44=0⇒4x2−x−4=0.\Rightarrow x^2 - \dfrac{1}{4}x + (-1) = 0 \\[1em] \Rightarrow x^2 - \dfrac{1}{4}x - 1 = 0 \\[1em] \Rightarrow \dfrac{4x^2 - x - 4}{4} = 0 \\[1em] \Rightarrow 4x^2 - x - 4 = 0.

Hence, required quadratic equation is 4x2 - x - 4 = 0.

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