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

Answer 1

Comparing $x^2+7x+12=0$ with $a{x}^2+bx+c=0$,
We get, $a=1,b=7andc=12.$
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.