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Questo esame si sostiene in inglese: le lezioni e le domande sono in inglese. L'interfaccia resta in italiano.
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Part 1 of 3
A quadratic equation in standard form is ax^2 + bx + c = 0 (a != 0). The discriminant Delta = b^2 - 4ac determines the number of real roots. If Delta > 0, there are two distinct real roots x = (-b +- sqrt(Delta)) / (2a).
Vieta's formulas state that the sum of the roots is x_1 + x_2 = -b / a and the product of the roots is x_1 * x_2 = c / a. Utilizing Vieta's relations allows you to verify roots rapidly without re-running the full quadratic formula.
Worked example
Solve x^2 - 7x + 12 = 0. Coefficients: a = 1, b = -7, c = 12. Vieta sum: x_1 + x_2 = 7. Vieta product: x_1 * x_2 = 12. Two numbers summing to 7 and multiplying to 12 are 3 and 4. Roots are x_1 = 3 and x_2 = 4. Checking Delta: 49 - 4(12) = 1 > 0 confirms two distinct real roots.
1.If the discriminant Delta is negative, a quadratic equation has zero real roots.
2.The sum of the roots of 2x^2 - 8x + 6 = 0 is equal to 8.
3.The product of the roots of x^2 - 5x + 6 = 0 equals 6.
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