# If the root of xÂ² + px + 12 = 0 are in the ratio 1:3 then what is the value of p ?

Let the roots of the given equation  = $\alpha, 3\alpha$

Now, According to the given equation

$\alpha + 3 \alpha = - p \\ and \alpha \times 3 \alpha = 12\\ \Rightarrow 4\alpha = -p\\ \alpha^{2} = 4\\ \alpha = +2, -2 \\$

put the value,

$4(2) = -p and 4(-2) = -p \\ \Rightarrow p = -8, +8$

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