Question 1: Roots of a Quadratic Equation and Inequality

April 2, 2026Mathematics

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April 2, 2026

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Question 1: Roots of a Quadratic Equation and Inequality

a) Given the equation $3x^2 - 4x + 2 = 0$ . The roots are $\alpha$ and $\beta$ . From Vieta's formulas, for a quadratic equation $ax^2 + bx + c = 0$ : Sum of roots: $\alpha + \beta = -\frac{b}{a} = -\frac{(-4)}{3} = \frac{4}{3}$ Product of roots: $\alpha\beta = \frac{c}{a} = \frac{2}{3}$

We need to show that $\alpha^3 + \beta^3 = -\frac{20}{27}$ .

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Question 1: Roots of a Quadratic Equation and Inequality a) Given the equation 3x^2 - 4x + 2 = 0.

Asked on April 2, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on April 2, 2026

Here are the solutions to the questions: Question 1: Roots of a Quadratic Equation and Inequality a) Given the equation 3x^2 - 4x + 2 = 0. The roots are and . From Vieta's formulas, for a quadratic equation ax^2 + bx + c = 0: Sum of roots: + = -(b)/(a) = -((-4))/(3) = (4)/(3) Product of roots: = (c)/(a) = (2)/(3) We need to show that ^3 + ^3 = -(20)/(27).