Find a quadratic polynomial with the given nu | vedclass

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Question

(A) Let the quadratic polynomial be $ax^2 + bx + c$ and its zeroes be $\alpha$ and $\beta$.Given that the sum of zeroes $\alpha + \beta = \frac{1}{4}$

Vedclass · Accepted Answer

$4x^2 - x - 4$

Vedclass · Answer

(A) Let the quadratic polynomial be $ax^2 + bx + c$ and its zeroes be $\alpha$ and $\beta$.Given that the sum of zeroes $\alpha + \beta = \frac{1}{4}$ and the product of zeroes $\alpha \beta = -1$.We know that a quadratic polynomial can be expressed as $k[x^2 - (\alpha + \beta)x + \alpha \beta]$,where $k$ is a non-zero constant.Substituting the given values,we get $k[x^2 - (\frac{1}{4})x + (-1)]$.To simplify,let $k = 4$.Then the polynomial becomes $4[x^2 - \frac{1}{4}x - 1] = 4x^2 - x - 4$.Thus,the required quadratic polynomial is $4x^2 - x - 4$.

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

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