If the sum of the zeros of a polynomial $x^{2} - (k + 3) x + (5 k - 3)$ is equal to one fourth of the product of zeros find the value of $k$ .

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Solution

For the polynomial $x^{2} - (k + 3) x + (5 k - 3)$

Sum of the roots $= - \frac{b}{a} = (k - 3)$

Product of the roots $= \frac{c}{a} = (5 k - 3)$

As per the question,
Sum of zeroes $= \frac{1}{4}$ ( product of zeroes)

$k - 3 = \frac{1}{4} (5 k - 3)$

$4 k - 12 = 5 k - 3$

$∴ k = - 9$

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