The roots of a quadratic equation are -3 and 1. Find its equation.
FURTHER MATHEMATICS
WAEC 2009
The roots of a quadratic equation are -3 and 1. Find its equation.
- A. \(x^{2} - 3x + 1 = 0\)
- B. \(x^{2} - 2x + 1 = 0\)
- C. \(x^{2} + 2x - 3 = 0\)
- D. \(x^{2} + x - 3 = 0\)
Correct Answer: C. \(x^{2} + 2x - 3 = 0\)
Explanation
Given the roots of an equation such that you can find the sum and product of the roots, the equation can be given as:
\(x^{2} - (\alpha + \beta)x + (\alpha \beta) = 0 \)
\(\alpha + \beta = -3 + 1 = -2\)
\(\alpha \beta = -3 \times 1 = -3\)
Equation: \(x^{2} - (-2)x + (-3) = 0 \implies x^{2} + 2x - 3 = 0\)
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