Question

If \(\alpha\) and \(\beta\) are the roots of \(x^2 - 5x + 6 = 0\), what is the value of \(\alpha^2 + \beta^2\)?

• A. 13
• B. 12
• C. 25
• D. 11

Hint:

Use (sum of roots) squared minus twice the product.

Answer 1

The Correct Option is A

Factor $x^2 - 5x + 6 = (x-2)(x-3)$, so the roots are $2$ and $3$. Then $\alpha^2 + \beta^2 = 2^2 + 3^2 = 4 + 9 = 13.$