Let the roots of the equation 3x2 - 4x + 2 = 0 be alpha and beta. Find the equation with integral coefficients whose roots are (1)/(alpha3) and (1)/(beta3).

April 10, 2026Mathematics

ScanSolve AI Answer

April 10, 2026

Answer

0 $are$ \alpha $and$ \beta$.

Here are the solutions to the questions:

Question 1 (Top Left): The roots of the equation $3x^2 - 4x + 2 = 0$ are $\alpha$ and $\beta$ . From Vieta's formulas: Sum of roots: $\alpha + \beta = -\frac{-4}{3} = \frac{4}{3}$ Product of roots: $\alpha \beta = \frac{2}{3}$

We need to find the equation with integral coefficients whose roots are $\frac{1}{\alpha^3}$ and $\frac{1}{\beta^3}$ . Let the new roots be $p = \frac{1}{\alpha^3}$ and $q = \frac{1}{\beta^3}$ .

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Question 1 (Top Left): The roots of the equation 3x^2 - 4x + 2 = 0 are and .

Asked on April 10, 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 10, 2026

Here are the solutions to the questions: Question 1 (Top Left): The roots of the equation 3x^2 - 4x + 2 = 0 are and . From Vieta's formulas: Sum of roots: + = -(-4)/(3) = (4)/(3) Product of roots: = (2)/(3) We need to find the equation with integral coefficients whose roots are (1)/(^3) and (1)/(^3). Let the new roots be p = (1)/(^3) and q = (1)/(^3).