Question

Given that \( \alpha_1, \alpha_2, \alpha_3 \) are the roots of \( 3x^3 - x^2 - 10x + 8 = 0 \), then the value of \( \alpha_1^2 + \alpha_2^2 + \alpha_3^2 \) is

• A. 9/61
• B. 61/9
• C. 16/9
• D. 9/16

Hint:

For cubic equations, use Vieta's formulas to relate the sum of squares of roots to the coefficients.

Answer 1

The Correct Option is B

Using the relations between the coefficients of a cubic equation and its roots, we find the value of \( \alpha_1^2 + \alpha_2^2 + \alpha_3^2 \) to be \( 61/9 \).