Question

x² -(1 + 2)x + 12 = 0
Solve the quadratic equation.​

Answer 1

Answer:

x

2

−

x

−

12

=

0

We can Split the Middle Term of this expression to factorise it and thereby find solutions.

In this technique, if we have to factorise an expression like  

a x 2 + b x + c

, we need to think of 2 numbers such that:

N 1 ⋅ N 2 = a ⋅ c = 1 ⋅ − 12 = − 12

 AND N 1 + N 2 = b = − 1

After trying out a few numbers we get  

N 1 = 3  and  N 2 = − 4  3 ⋅ − 4 = − 12 , and  3 + ( −4 ) = − 1  x 2 − x − 12 = x 2 − 4 x + 3 x − 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

Step-by-step explanation: