If one of the factors of $x^{2} + x - 20$ is $(x + 5)$ , then other factor is

(x - 4)

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(x - 5)

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(x - 6)

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(x - 7)

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Solution

The correct option is A $(x - 4)$
Let $(x - a)$ be the other factor.
Now, $(x + 5), (x - a)$ are factors of the quadratic equation $x^{2} + x - 20$
Thus,
$(x + 5) (x - a) = x^{2} + x - 20$
$=> x^{2} - a x + 5 x - 5 a = x^{2} + x - 20$
$=> x (5 - a) - 5 a = x - 20$
Now, considering the co-efficients of $x$ on the both sides,
$5 - a = 1$
$=> a = 5 - 1 = 4$
Therefore the other factor is $(x - 4)$

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