Question

If the roots of the quadratic equation $ 2x^2 - 3x + 1 = 0 $ are $ \alpha $ and $ \beta $, what is the value of $ \alpha^2 + \beta^2 $?

• A. $ \frac{1}{4} $
• B. $ \frac{5}{4} $
• C. $ \frac{9}{4} $
• D. $ \frac{7}{4} $

Hint:

Use Vieta's formulas to find expressions involving roots without solving the quadratic explicitly.

Answer 1

The Correct Option is B

Given: Quadratic equation $ 2x^2 - 3x + 1 = 0 $
Let roots be $ \alpha $ and $ \beta $. Using Vieta’s formulas: $$ \alpha + \beta = \frac{3}{2}, \quad \alpha \beta = \frac{1}{2} $$
Use identity: $$ \alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta $$
Substituting values: $$ \alpha^2 + \beta^2 = \left( \frac{3}{2} \right)^2 - 2 \cdot \frac{1}{2} = \frac{9}{4} - 1 = \frac{5}{4} $$