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Roots of a Quadratic Equation

If -1 and 3 a...

Question

If -1 and 3 are the roots of $x^{2} + p x + q = 0,$ find the values of p and q.

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Solution

Since -1 is a root,

$(- 1)^{2} + p (- 1) + q = 0 \Rightarrow - p + q = - 1 . . . (1)$

Since 3 is a root,

$3^{2} + 3 p + q = 0 \Rightarrow 3 p + q = - 9 . . . (2)$

Subtracting equation (2) from equation (1), $- 4 p = 8 \Rightarrow p = - 2$

Substituting this in equation (1), $2 + q = - 1 \Rightarrow q = - 3$

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