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Question
If x2−4x−12=(x+m)(x+n), then the value of (m+n) is _____.
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Solution
We know that,
(x+a)(x+b)=x2+(a+b)x+ab
x2−4x−12=x2+(−6+2)x+(−6×2)=(x−6)(x+2)=(x+m)(x+n)
By comparison of (x−6)(x+2) with (x+m)(x+n), we get m=−6 and n=2.
Hence, m+n=−6+2=−4
(x+a)(x+b)=x2+(a+b)x+ab
x2−4x−12=x2+(−6+2)x+(−6×2)=(x−6)(x+2)=(x+m)(x+n)
By comparison of (x−6)(x+2) with (x+m)(x+n), we get m=−6 and n=2.
Hence, m+n=−6+2=−4
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