Determine the nature of the roots of the quadratic equation: 3x² - 4x + 2 = 0.
Answer and explanation
Correct answer: B. two complex conjugate non-real roots
- Step 1: Identify coefficients: a = 3, b = -4, c = 2. Step 2. Calculate discriminant: Δ = b² - 4ac = (-4)² - 4(3)(2) = 16 - 24 = -8. Step 3. Since Δ < 0, the equation has no real roots (two complex conjugate roots). Answer: two complex conjugate non-real roots. Why not the others: Real distinct roots require Δ > 0; real equal roots require Δ = 0; rational roots require Δ to be a positive perfect square.
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