Question

What is the nature of the 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 \( D>0 \), the roots are real and unequal. If \( D = 0 \), the roots are real and equal. If \( D<0 \), the roots are not real (complex).

Answer 1

The Correct Option is C

Step 1: Compute the discriminant For a quadratic equation \( ax^2 + bx + c = 0 \), the discriminant is: \[ D = b^2 - 4ac \] Substituting \( a = 6 \), \( b = -3 \), and \( c = 5 \): \[ D = (-3)^2 - 4(6)(5) \] \[ = 9 - 120 \] \[ = -111 \] Step 2: Interpret the discriminant Since \( D<0 \), the roots are not real. Thus, the correct answer is **"Not real"**.