The original equation is 2x2 - 5x - 3 = 0.

April 17, 2026Mathematics

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April 17, 2026

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The original equation is $2x^2 - 5x - 3 = 0$ . Let the roots of this equation be $\alpha$ and $\beta$ . Using Vieta's formulas: Sum of roots: $\alpha + \beta = -\frac{(-5)}{2} = \frac{5}{2}$ Product of roots: $\alpha \beta = \frac{-3}{2}$

The general form of a quadratic equation with roots $r_1$ and $r_2$ is $x^2 - (r_1 + r_2)x + r_1 r_2 = 0$ . We will multiply by a common denominator to ensure integer coefficients.

*a) (i) Roots are $\frac{1}{\alpha

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The original equation is 2x^2 - 5x - 3 = 0. Let the roots of this equation be and .

Asked on April 17, 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 17, 2026

The original equation is 2x^2 - 5x - 3 = 0. Let the roots of this equation be and . Using Vieta's formulas: Sum of roots: + = -((-5))/(2) = (5)/(2) Product of roots: = (-3)/(2) The general form of a quadratic equation with roots r_1 and r_2 is x^2 - (r_1 + r_2)x + r_1 r_2 = 0. We will multiply by a common denominator to ensure integer coefficients. *a) (i) Roots are $1