WAEC - Mathematics (2024 - No. 19)
Find the quadratic equation whose roots are \(\frac{2}{3}\) and - 1
3x\(^2\) - x - 2 = 0
3x\(^2\) + x + 2 = 0
3x\(^2\) + x - 2 = 0
3x\(^2\) + x - 1 = 0
Explanation
The roots are \(\frac{2}{3}\) and - 1
Using x\(^2\) - (α + β)x + αβ = 0
α + β = \(\frac{2}{3}\) + (-1) = \(\frac{2}{3}\) - 1 = \(\frac{-1}{3}\)
αβ = \(\frac{2}{3}\) x (-1) = \(\frac{-2}{3}\)
x\(^2\) - (\(\frac{-1}{3}\) )x + (\(\frac{-2}{3}\)) = 0
multiply through by 3
3x\(^2\) + x - 2 = 0
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