Question

The roots of equation \( 4x^2 - 12x + 9 = 0 \) will be:

• A. Real and unequal
• B. Not real
• C. Real and equal
• D. Zero

Hint:

If the discriminant \( \Delta = 0 \), the roots of the quadratic equation are real and equal.

Answer 1

The Correct Option is C

To find the nature of the roots of the quadratic equation \( 4x^2 - 12x + 9 = 0 \), we use the discriminant formula: \[ \Delta = b^2 - 4ac \] For the given equation \( 4x^2 - 12x + 9 = 0 \), we have: - \( a = 4 \) - \( b = -12 \) - \( c = 9 \) Substitute these values into the discriminant formula: \[ \Delta = (-12)^2 - 4 \times 4 \times 9 = 144 - 144 = 0 \]
Step 1: Conclusion.
Since the discriminant \( \Delta = 0 \), the roots of the equation are real and equal.