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Question

If (x+a)(x+b)=x2+5x+6,what is the value of (a−b) if (a−b)>0?

A
2
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B
1
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C
3
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D
4
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Solution

The correct option is B 1
We know that, (x+a)(x+b)=x2+(5)x+(6)

By splitting the middle term, x2+(5)x+(6) such that, the product is equal to 6 and sum or difference is equal to +5.


Hence, x2+5x+6=x2+3x+2x+6

Taking out the common factor,x(x+3)+2(x+3)(x+3)(x+2)

Comparing to (x+a)(x+b) and also given that (ab)>0.

Hence a=3 and b=2
ab=1

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