Question

If \( \alpha \) and \( \beta \) are the roots of the quadratic equation \( x^2 + 6x + 5 = 0 \), then the value of \( \alpha^2 + \beta^2 \) is:

• A. \( 30 \)
• B. \( 16 \)
• C. \( 26 \)
• D. \( 20 \)

Hint:

The identity: \[ \alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta \] is useful in quadratic problems.

Answer 1

The Correct Option is C

Using the identity:
\[ \alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta \] For \( x^2 + 6x + 5 = 0 \):
\[ \alpha + \beta = -6, \quad \alpha \beta = 5 \] \[ \alpha^2 + \beta^2 = (-6)^2 - 2(5) = 36 - 10 = 26 \]