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

**Solution: **

Given:

**Quadratic equation is x ^{2} + x - 20 = 0 which is in the form of ax^{2} + bx + c = 0**

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

**We know that if one factor of the quadratic equation ax ^{2} + bx + c = 0 is (x + p) then the other factor will be (x - q)**

⇒ (x - q)(x + p) = ax^{2} + 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) = x ^{2} + x - 20 (Now solving the equation )**

⇒ x^{2} - ax + 5x - 5a = x^{2} + x - 20

(x^{2 }is on the both sides with same sign so it will get cancelled)

⇒ 5x - ax - 5a = x^{2} + 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 x^{2} + x - 20 is (x + 5), then the other factor is?

**Summary:**

The two factors of the quadratic equation x^{2} + x - 20 are (x + 5) and (x - 4).

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