Question

If a and b are the roots of the equation x² - 6x + 6=0, then the value of a² + b² is

• A. 36
• B. 24
• C. 12
• D. 6

Answer 1

The Correct Option is B

We have given the equation, \(x^2 - 6x +6 = 0\)

So, the Sum of roots = \(a + b = 6\) – (i)

Product of roots = \(ab = 6\)

Squaring both sides in equation (i)

\((a + b)^2 = (6)^2\)

\(a^2 + b^2 + 2ab = 36\)

\((a^2 + b^2) + 2(6) = 36\) as product of \(ab = 36\)

\((a^2 + b^2) = 36 - 12 = 24\)

So, \((a^2 + b^2) = 24\)

The correct option is (B): 24