Multiple choice

If a and b are the roots of the equation $x^2-6x+6=0$, then the value of $a^2+b^2$ are :

  1. 6

  2. 12

  3. 24

  4. 36
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For x^2 - 6x + 6 = 0, a + b = 6 and ab = 6. a^2 + b^2 = (a + b)^2 - 2ab = 6^2 - 2 * 6 = 36 - 12 = 24.

AI explanation

Using Vieta's formulas for the roots a and b, the sum a plus b equals 6 and the product ab equals 6. The identity for the sum of squares states a squared plus b squared equals the square of the sum minus twice the product. Substituting the values gives 6 squared minus 2 times 6, which equals 36 minus 12, resulting in 24.

Keep practicing — related questions