Question

If \( \alpha \) and \( \beta \) are the roots of the quadratic equation \( x^2 - 8x + 5 = 0 \), then the value of \( \alpha^2 + \beta^2 \) is:

• A. \( 44 \)
• B. \( 54 \)
• C. \( 74 \)
• D. \( 64 \)

Hint:

For any quadratic equation \( ax^2 + bx + c = 0 \): \[ \alpha + \beta = -\frac{b}{a}, \quad \alpha\beta = \frac{c}{a}. \] \[ \alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta. \]

Answer 1

The Correct Option is B

Using the identity: \[ \alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta. \] From the quadratic equation: \[ \alpha + \beta = -\frac{(-8)}{1} = \] \[ \alpha\beta = \frac{5}{1} = 5. \] \[ \alpha^2 + \beta^2 = 8^2 - 2(5). \] \[ = 64 - 10 = \]