Find the roots of the quadratic equation by factorization: 2x² + 5x - 3 = 0.
Answer and explanation
Correct answer: D. x = 1/2 or x = -3
- Step 1: Multiply a and c: 2 × (-3) = -6. Find two numbers that multiply to -6 and add to +5: +6 and -1. Step 2. Split middle term: 2x² + 6x - x - 3 = 0. Step 3. Factor by grouping: 2x(x + 3) - 1(x + 3) = 0 => (2x - 1)(x + 3) = 0. Step 4. Solve: 2x - 1 = 0 => x = 1/2; x + 3 = 0 => x = -3. Answer: x = 1/2 or x = -3. Why not the others: Inverted signs in the option x = -1/2 or x = 3; incorrect factorization in the options x = 1 or x = -3 and x = 2 or x = -3/2.
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