Question

What is the nature of roots of the quadratic equation \( 6x^2 - 3x + 5 = 0 \)?

• A. Real and unequal
• B. Real and equal
• C. Not real
• D. None of these

Hint:

If \( D>0 \), roots are real and unequal. If \( D = 0 \), roots are real and equal. If \( D<0 \), roots are not real.

Answer 1

The Correct Option is C

The nature of roots is determined using the discriminant: \[ D = b^2 - 4ac \] For \( 6x^2 - 3x + 5 = 0 \):
\[ D = (-3)^2 - 4(6)(5) = 9 - 120 = -111 \] Since \( D<0 \), the roots are not real.