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Question

Find the number of integers that lie between the roots of the equation x2+7x+12=0.

A
1
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B
7
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C
12
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Solution

Comparing x2+7x+12=0 to ax2+bx+c=0, we get a = 1, b = 7 and c = 12.

Applying factorization method to find the roots,

We need to find two numbers whose product is 12 i.e., (a×c) and whose sum is 7 i.e., (b)

Pairs of numbers whose product is 12 are
(2,6),(2,6),(4,3),(4,3),(1,12) and (1,12).

Identifying the pair, we rewrite the given quadratic equation x2+7x+12 as


x2+4x+3x+12=x(x+4)+3(x+4)
(x+4) (x+3)=0
(x+4)=0 or (x+3)=0
x=4,3

Roots of x2+7x+12 are 4 and 3.

No. of integers between -4 and -3 is 0.

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