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If one zero of the polynomial $p(x) = 6x^2 + 37x – (k – 2)$ is reciprocal of the other, then find the value of $k$.
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Sol. $p(x) = 6x^2 + 37x - (k – 2)$
Let the zeroes be $\alpha, \frac{1}{\alpha}$
Product of zeroes = $\alpha . \frac{1}{\alpha} = \frac{-(k-2)}{6}$
$1 = \frac{-(k-2)}{6}$
$6 = -k + 2 \Rightarrow k = -4$
Let the zeroes be $\alpha, \frac{1}{\alpha}$
Product of zeroes = $\alpha . \frac{1}{\alpha} = \frac{-(k-2)}{6}$
$1 = \frac{-(k-2)}{6}$
$6 = -k + 2 \Rightarrow k = -4$