Question

Solve the following quadratic equation:

3x² – 2x – 1 = 0

Answer 1

We write, –2x = –3x + x as 3x² × (–1) = –3x² = (–3x) × x 

∴ 3x² – 2x – 1 = 0

⇒ 3x² – 3x + x – 1 = 0 

⇒ 3x(x – 1) + 1(x – 1) = 0 

⇒ (x – 1)(3x + 1) = 0 

⇒ x – 1 = 0 or 3x + 1 = 0 

⇒ x = 1 or x = `(-1)/3` 

Hence, the roots of the given equation are 1 and `(-1)/3`.