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A quadratic equation in standard form is ax2 + bx + c = 0 (a ≠ 0). The discriminant Δ = b2 - 4ac determines the number of real roots. If Δ > 0, there are two distinct real roots x = (-b ± √(Δ)) / (2a).
Vieta's formulas state that the sum of the roots is x1 + x2 = -b / a and the product of the roots is x1 × x2 = c / a. Utilizing Vieta's relations allows you to verify roots rapidly without re-running the full quadratic formula.
Worked example
1.If the discriminant Δ is negative, a quadratic equation has zero real roots.
2.The sum of the roots of 2x2 - 8x + 6 = 0 is equal to 8.
3.The product of the roots of x2 - 5x + 6 = 0 equals 6.
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