Question

What is the nature of the roots of the equation, 2x² – 6x + 3 = 0?

Options

• rational and unequal

• irrational and unequal

• real and equal

• imaginary and unequal

Answer 1

Irrational and Unequal

Explanation:

For 2x² – 6x + 3 = 0,

a = 2, b = –6, c = 3. 

Discriminant D = b² – 4ac

= (–6)² – 4 × 2 × 3 

= 36 – 24

= 12 > 0, so the roots are real and distinct. 

The roots are `x = (3 ± sqrt(3))/2` since `sqrt(12) = 2sqrt(3)` and because `sqrt(3)` is irrational the roots are irrational and unequal.