Given that $\alpha$ and $\beta$ are the roots of an equation such that $\alpha + \beta = 3$ and $\alpha \beta = 2$, find the equation.

Assessment: WAEC SSCE - Further Mathematics - 2007 (Objective) Subject: Further Mathematics

Question 1 Report

$x^{2} - 3x + 2 = 0$

$x^{2} - 2x + 3 = 0$

$x^{2} - 3x - 2 = 0$

$x^{2} - 2x - 3 = 0$

Answer Details

We are given that $\alpha$ and $\beta$ are the roots of the equation, and we are also given two conditions based on these roots: 1. $\alpha + \beta = 3$ 2. $\alpha \beta = 2$ To find the equation, we can use the fact that if $\alpha$ and $\beta$ are roots of the equation, then the equation can be written in factored form as: $$(x - \alpha)(x - \beta) = 0$$ Expanding this equation, we get: $$x^2 - (\alpha + \beta)x + \alpha\beta = 0$$ Substituting the values of $\alpha + \beta$ and $\alpha \beta$ from the given conditions, we get: $$x^2 - 3x + 2 = 0$$ Therefore, the equation with roots $\alpha$ and $\beta$ is: $$x^2 - 3x + 2 = 0$$ Hence, the correct option is (a) $x^{2} - 3x + 2 = 0$.

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Given that \(\alpha\) and \(\beta\) are the roots of an equation such that \(\alpha + \beta = 3\) and \(\alpha \beta = 2\), find the equation.

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Given that \(\alpha\) and \(\beta\) are the roots of an equation such that \(\alpha + \beta = 3\) and \(\alpha \beta = 2\), find the equation.

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