Question

How do you solve x²−x−20=0?

Answer 1

Answer:

Find two numbers whose product is 20

and whose difference is 1.The pair 5, 4

works.

hence

x2−x−20=(x−5)(x+4).

So solutions are

x=5 or x=−4.

Explanation:

(x−a)(x+b)=x2−(a−b)x−ab

Matching this against x2−x−20 we see that if we can find a and b such that a−b=1 and ab=20 ,then we can factor the quadratic into two linear terms.

The pair

a=5 , b=4

works, giving us

x2−x−20=(x−5)(x+4)

This will be 0 when

(x−5)=0 or (x+4)=0.

which is when

x=5 or x=−4.