Question

Solve the equation.

x2 − x − 12 = 0
A) x = 4
B) x = −3
C) x = −3 or x = 4
D) x = −4 or x = 3

Answer 1

C

Explanation:

In this technique, if we have to factorise an expression like ax2+bx+c, we need to think of 2 numbers such that:

N1⋅N2=a⋅c=1⋅−12=−12

AND

N1+N2=b=−1

After trying out a few numbers we get N1=3 and N2=−4

3⋅−4=−12, and 3+(−4)=−1

x2−x−12=x2−4x+3x−12

x(x−4)+3(x−4)=0

(x+3)(x−4)=0

Now we equate the factors to zero.

x+3=0,x=−3

x−4=0,x=4