If the polynomial $g (x) = x^{2} + 5 x + k$ is a factor of $p (x) = 4 x^{4} + 20 x^{3} - 26 x^{2} - 10 x + 12$ then find the value of k. Also find all the zeroes of the polynomial.

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Solution

Ans: $k = - 6$
Zeroes of $p (x) = - 6, 1,$ $\frac{1}{\sqrt{2}}, - \frac{1}{\sqrt{2}}$

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