Question

Find the number of integers that lie between the roots of the equation $x^2+7x+12=0$

• A. 1
• B. 7
• C. 12
• D. 0

Answer 1

The correct option is D

0

Comparing $x^2+7x+12=0$to$a{x}^2+bx+c=0$, we have a = 1 , b = 7 and c = 12.
Applying facorization method to find the roots,
We need to find two numbers whose product is 12 i.e. ($a\times c$) and whose sum is 7 i.e. ($b$)
Pairs of numbers whose product is 12
2,6
-2 ,-6
4,3
-4, -3
1, 12
-1, -12
Identifying the pair, we rewrite the given quadratic equation as
$x^2+7x+12$
$\Rightarrow x^2+4x+3x+12=x(x+4)+3(x+4)$
$\Rightarrow (x+4)(x+3)=0$
$\Rightarrow (x+4)=0or(x+3)=0$
$\Rightarrow x=-4,-3$
No. of integers between -4 and -3 is 0.