Find the number of integers that lie between the roots of the equation x2+7x+12=0
0
Comparing x2+7x+12=0 to ax2+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×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
x2+7x+12
⇒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
No. of integers between -4 and -3 is 0.