Question

Solve the quadratic equation: \( 2x^2 + 5x - 3 = 0 \)

Hint:

Always compute the discriminant first to understand the nature of roots and prevent under-root mistakes.

Answer 1

Step 1: Identify coefficients: \[ a = 2, \quad b = 5, \quad c = -3 \] Step 2: Use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Step 3: Calculate discriminant: \[ D = b^2 - 4ac = 25 + 24 = 49 \] Step 4: Compute roots: \[ x = \frac{-5 \pm \sqrt{49}}{4} = \frac{-5 \pm 7}{4} \] \[ x_1 = \frac{-5 + 7}{4} = \frac{2}{4} = \frac{1}{2}, \quad x_2 = \frac{-5 - 7}{4} = \frac{-12}{4} = -3 \] Final Answer: \[ \boxed{x = \frac{1}{2}, \quad x = -3} \]