How do you solve x²−x−20=0?
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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.
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