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Solving a Quadratic Equation by Completion of Squares Method

For what valu...

Question

For what value of p, is $(- 4)$ a zero of the polynomial $p (x) = x^{2} - 2 x - (7 p + 3)$ ?

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Solution

$p (x) = x^{2} - 2 x - (7 p + 3)$

If $- 4$ is a zero of the polynomial,

$p (- 4) = 0$

$(- 4)^{2} - 2 (- 4) - (7 p + 3) = 0$

$16 + 8 - (7 p + 3) = 0$

$16 + 8 = 7 p + 3$

$7 p = 21$

$p = 3$

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