Obtain a quadratic polynomial p(x) = ax^2 + b | vedclass

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Question

(C) quadratic polynomial is given by the formula $p(x) = k[x^2 - (	ext{sum of zeros})x + (	ext{product of zeros})]$,where $k$ is a non-zero constant

Vedclass · Accepted Answer

$k(-x^2 + \sqrt{2}x - \frac{1}{3})$

Vedclass · Answer

(C) quadratic polynomial is given by the formula $p(x) = k[x^2 - (	ext{sum of zeros})x + (	ext{product of zeros})]$,where $k$ is a non-zero constant.Given that the sum of zeros is $\sqrt{2}$ and the product of zeros is $\frac{1}{3}$,we substitute these values into the formula:$p(x) = k[x^2 - (\sqrt{2})x + \frac{1}{3}]$Since the condition $a $p(x) = k[-x^2 + \sqrt{2}x - \frac{1}{3}]$Thus,the required polynomial is $k(-x^2 + \sqrt{2}x - \frac{1}{3})$.

Obtain a quadratic polynomial $p(x) = ax^2 + bx + c$,where the sum of zeros is $\sqrt{2}$ and the product of zeros is $\frac{1}{3}$,given that $a < 0$.

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