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 $x^2+7x+12=0toa{x}^2+bx+c=0$, 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., ($a\times c$) 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 $x^2+7x+12$ as


$\Rightarrow x^2+4x+3x+12=x(x+4)+3(x+4)$
$\Rightarrow (x+4)(x+3)=0$
$\Rightarrow (x+4)=0or(x+3)=0$
$\Rightarrow x=-4,-3$

$\therefore$ Roots of $x^2+7x+12$ are $-4$ and $-3$.

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