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Relationship between Zeroes and Coefficients of a Polynomial

The roots x...

Question

The roots $x_{1}$ and $x_{2}$ of the equation $x^{2} + p x + 12 = 0.$ are such that $x_{2} - x_{1} = 1$ Find p.

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Solution

$x^{2} + p x + 12 = 0 s u m o f r o o t s = x_{1} + x_{2} = 12 x_{2} - x_{1} = 1 {(x_{1} + x_{2})}^{2} = {(x_{2} - x_{1})}^{2} + 4 x_{1} x_{2} p^{2} = 1 + 48 p^{2} = 49 p = \pm 7$

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