Question

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

• A. rational and equal
• B. irrational
• C. rational and unequal
• D. not real

Hint:

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

Answer 1

The Correct Option is B

Step 1: Recall the discriminant formula.
For a quadratic equation \(ax^2 + bx + c = 0\), the discriminant (\(D\)) is given by \[ D = b^2 - 4ac \]
Step 2: Substitute the values.
Here, \(a = 2\), \(b = 5\), \(c = 4\). \[ D = (5)^2 - 4(2)(4) = 25 - 32 = -7 \]
Step 3: Analyze the discriminant.
Since \(D<0\), the roots are not real. Therefore, the equation has no real roots.
Step 4: Conclusion.
The correct answer is (D) not real.