Question

The nature of the roots of the equation \( 2x^2 - 5x + 4 = 0 \) will be:

• A. Real and equal
• B. Imaginary (not real)
• C. Real and distinct
• D. None of these

Hint:

Always check the discriminant \( D = b^2 - 4ac \) to determine the nature of roots before solving a quadratic equation.

Answer 1

The Correct Option is B

Step 1: Recall the discriminant formula.
For a quadratic equation \( ax^2 + bx + c = 0 \), \[ D = b^2 - 4ac \] If \( D>0 \): roots are real and distinct.
If \( D = 0 \): roots are real and equal.
If \( D<0 \): roots are imaginary (not real).

Step 2: Substitute values.
Here, \( a = 2 \), \( b = -5 \), \( c = 4 \). \[ D = (-5)^2 - 4(2)(4) = 25 - 32 = -7 \]
Step 3: Analyze discriminant.
Since \( D<0 \), the roots are imaginary (not real).
Step 4: Final answer.
The roots are imaginary.