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)

We know that if one factor of the quadratic equation ax² + bx + c = 0 is (x + p) then the other factor will be (x - q)

⇒ (x - q)(x + p) = ax² + bx + c = 0 --- (1)

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

Now,

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

(x + 5)(x - a) = x² + x - 20 (Now solving the equation )

⇒ x² - ax + 5x - 5a = x² + x - 20

(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

Therefore, the other factor is (x - 4).

---

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).