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If one root of the quadratic equation $x^2 + 12x - k = 0$ is thrice the other root, then find the value of $k$.
If one root of the quadratic equation $x^2 + 12x - k = 0$ is thrice the other root, then find the value of $k$.
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$x^2 + 12x - k = 0$
Let the roots be $\alpha, 3\alpha$
$\alpha + 3\alpha = -12 \Rightarrow \alpha =-3$
$\alpha.3\alpha=-k \Rightarrow 3\alpha^2 = -k$
$\Rightarrow k = -27$
Let the roots be $\alpha, 3\alpha$
$\alpha + 3\alpha = -12 \Rightarrow \alpha =-3$
$\alpha.3\alpha=-k \Rightarrow 3\alpha^2 = -k$
$\Rightarrow k = -27$