Question

The roots of the equation x2 – 14x + 48 = 0 are

Answer 1

The roots of this equation will be x = 6 or x = 8.

You can solve this equation by factorising:

x² - 14x + 48 = 0

Factors of 48:

1 and 48

2 and 24

3 and 16

4 and 12

6 and 8

Because the x-coefficient is negative but the value at the end is positive, we know that both numbers in the brackets must be negative (i.e. (x - a)(x - b) ), so we need to find 2 numbers from the list of factors that when negative and added together give -14. In this case it is -6 and -8.

Therefore your final factorisation is (x - 6)(x - 8) = 0, which gives the solutions x = 6 or x = 8.

I hope this helps! Let me know if you have any questions :)