Find a quadratic polynomial,each with the giv | vedclass

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Question

(A) Let the quadratic polynomial be $p(x) = ax^2 + bx + c$,and its zeroes be $\alpha$ and $\beta$.The sum of zeroes is given by $\alpha + \beta = -\fr

Vedclass · Accepted Answer

$4x^2 + x + 1$

Vedclass · Answer

(A) Let the quadratic polynomial be $p(x) = ax^2 + bx + c$,and its zeroes be $\alpha$ and $\beta$.The sum of zeroes is given by $\alpha + \beta = -\frac{1}{4} = -\frac{b}{a}$.The product of zeroes is given by $\alpha 	imes \beta = \frac{1}{4} = \frac{c}{a}$.Comparing the ratios,if we take $a = 4$,then $b = 1$ and $c = 1$.Substituting these values into the general form $ax^2 + bx + c$,we get the polynomial $4x^2 + x + 1$.

Find a quadratic polynomial,each with the given numbers as the sum and product of its zeroes respectively: $-\frac{1}{4}, \frac{1}{4}$.

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