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

Step 1: Read off sum and product of roots.
For \(x^2 - 5x + 6 = 0\): \(\alpha + \beta = 5\), \(\alpha\beta = 6\).
Step 2: Use the identity.
\[\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta\] Step 3: Substitute.
\[= 5^2 - 2(6) = 25 - 12 = \boxed{13}\]