If one of the factors of x² + x - 20 is (x + 5), then the other factor is?

Solution:

Given:

Quadratic equation is x² + x - 20 = 0 which is in the form of ax² + bx + c = 0

Now one factor of the equation is given as (x + 5)

Let us assume the other factor as (x - a)

Now,

(x + 5) and (x - a) are the factors of the given equation.

Therefore,

(x + 5) (x - a) = x² + x - 20

(Now solving the equation)

⇒  x² - ax + 5x - 5a = x² + x - 20 (Since, x² is on the both sides with same sign so it will get cancelled)

⇒  5x - ax - 5a = x² + x - 20

⇒  (5 - a) x - 5a = x - 20

Now, by equating the coefficients of x, we get

⇒ 5 - a = 1

⇒ 5 - 1 = a

⇒ a = 4

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If one of the factors of x² + x - 20 is (x + 5), then the other factor is?

Summary:

The two factors of the quadratic equation x² +x - 20 are (x + 5) and (x - 4).