Without solving, find the sum of the roots of the quadratic equation $4 x^{2} - 9 x + 2 = 0$ .

medium 2 marks Class 10 · Mathematics · Quadratic Equations

Answer

9/4

The correct answer is 9/4 — Apply the formula: $α + β = - \frac{- 9}{4} = \frac{9}{4}$ .

Step-by-step solution

For a quadratic $a x^{2} + b x + c = 0$ , the sum of the roots $α + β = - \frac{b}{a}$ .
Identify $a = 4$ and $b = - 9$ from the given equation.
Apply the formula: $α + β = - \frac{- 9}{4} = \frac{9}{4}$ .

Common mistake: Using

\frac{b}{a}

instead of

- \frac{b}{a}

, giving

- 9/4

Concept tested: Sum of roots (Vieta’s formula)