A quadratic equation has roots α and β such that α + β = 3 and αβ = -10. Which of the following is the equation?
A$x^2 - 3x - 10 = 0$CORRECT
B$x^2 + 3x - 10 = 0$
C$x^2 - 3x + 10 = 0$
D$x^2 + 3x + 10 = 0$
GCEMathematicsQuadratic Equations2021
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Why the answer is A, and why the others tempt you.
A quadratic with roots α and β is x² - (α + β)x + αβ = 0. Substituting α + β = 3 and αβ = -10 gives x² - 3x + (-10) = 0, which is x² - 3x - 10 = 0. Option B has the wrong sign on the middle term, a common error.
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