You're not done with the first question, you were to show that 2b2=9c

April 24, 2026Mathematics

ScanSolve AI Answer

April 24, 2026

Answer

-\frac{b}{2} \quad (1) $$

Step 1: Apply Vieta's formulas for the given quadratic equation. For the quadratic equation $2x^2 + bx + c = 0$ , the sum of the roots ( $\alpha + \beta$ ) and the product of the roots ( $\alpha \beta$ ) are given by: $\alpha + \beta = -\frac{b}{2} \quad (1)$ $\alpha \beta = \frac{c}{2} \quad (2)$

Step 2: Use the given condition $\alpha = 2\beta$ in the sum of roots equation. Substitute $\alpha = 2\beta$ into equation (1): $2\beta + \beta = -\frac{b}{2}$

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Apply Vieta's formulas for the given quadratic equation.

Asked on April 24, 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 24, 2026

Step 1: Apply Vieta's formulas for the given quadratic equation. For the quadratic equation 2x^2 + bx + c = 0, the sum of the roots ( + ) and the product of the roots ( ) are given by: + = -(b)/(2) (1) = (c)/(2) (2) Step 2: Use the given condition = 2 in the sum of roots equation. Substitute = 2 into equation (1): 2 + = -(b)/(2) 3