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Solving a Quadratic Equation by Factorization Method

The equations...

Question

The equations $x^{2} - p x + 6 = 0$ and $x^{2} + 2 x - r = 0$ one root as $3$ , then value of $p$ and $r$ are

3, 6

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5, 15

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2, 3

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3, - 5

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Solution

The correct option is C $5, 15$
$f (x) = x^{2} - p x + 6 f (3) = 0 3^{2} - 3 p + 6 = 0 - 3 p = - 15 p = 5 g (x) = x^{2} + 2 x - r g (3) = 0 3^{2} + 2.3 - 4 = 0 r = 15$

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Let r be a root of the equation $x^{2}$ + 2x + 6 = 0. The value of (r + 2) (r + 3) (r + 4) (r + 5) is equal to.

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