Question

If x = k is a solution of the equation x(3x – 7) – 10 = 0, then find the value of k.

Answer 1

Given:

x(3x – 7) – 10 = 0

⇒ 3x² − 7x − 10 = 0

Find two numbers that:

Multiply to 3 × (−10) = −30

Add to −7

The numbers are –10 and 3

3x² − 10x + 3x − 10 = 0

⇒ (3x² + 3x) − (10x + 10) = 0

⇒ 3x(x + 1) − 10(x + 1) = 0

3x − 10 = 0

⇒ x = `10/3`

x + 1 = 0

⇒ x = −1

`k = 10/3 or k = -1`