Question

Solve the following quadratic equation by factorisation method:

m² + 14m + 13 = 0

Answer 1

Given: m² + 14m + 13 = 0 

Find two numbers whose sum is 14 and product is 13.

We need to find two numbers a and b such that: 

a + b = 14

a × b = 13

The two numbers that satisfy these conditions are 1 and 13 because:

1 + 13 = 14

1 × 13 = 13

Split the middle term

m² + m + 13m + 13 = 0

m(m + 1) + 13(m + 1) = 0

(m + 1)(m + 13) = 0

Set each factor equal to zero.

m + 1 = 0 or m + 13 = 0 

m = −1 or m = −13