Question

Discriminant and nature of the roots

3x2 – 4x – 2 = 0
5x2 – 1 = 0
2x2 – 5x + 4 = 0
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Answer 1

see explanation

Explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 ) , then the discriminant is

Δ = b² - 4ac

• If b² - 4ac > 0 then roots are real and distinct

• If b² - 4ac = 0 then roots are real and equal

• If b² - 4ac < 0 then roots are not real

3x² - 4x - 2 = 0 ← is in standard form

with a = 3, b = - 4, c = - 2 , thus

b² - 4ac = (- 4)² - (4 × 3 × - 2) = 16 - ( - 24) = 16 + 24 = 40

Since b² - 4ac > 0 then roots are real and distinct