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Mathematics

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

0,50, \sqrt{5}

Polynomials

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Answer

For given roots,

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

Substituting values we get :

⇒x2−0x+5=0⇒x2−0+5=0⇒x2+5=0.\Rightarrow x^2 - 0x + \sqrt{5} = 0 \\[1em] \Rightarrow x^2 - 0 + \sqrt{5} = 0 \\[1em] \Rightarrow x^2 + \sqrt{5} = 0.

Hence, required quadratic equation is x2+5=0.x^2 + \sqrt{5} = 0.

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