Question

The discriminant of the quadratic equation \(ax^2 + x + a = 0\) is :

• A. \(\sqrt{1 - 4a^2}\)
• B. \(1 - 4a^2\)
• C. \(4a^2 - 1\)
• D. \(\sqrt{4a^2 - 1}\)

Hint:

Remember that the discriminant itself does not include the square root symbol. The square root is part of the quadratic formula (\(\sqrt{D}\)), but the discriminant is just the expression inside it.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The discriminant (\(D\)) of a quadratic equation helps determine the nature of its roots. For an equation in the form \(Ax^2 + Bx + C = 0\), the discriminant is the value under the square root in the quadratic formula.
Step 2: Key Formula or Approach:
\[ D = B^2 - 4AC \]
Step 3: Detailed Explanation:
1. Identify the coefficients from the given equation \(ax^2 + 1x + a = 0\):
- \(A = a\)
- \(B = 1\)
- \(C = a\)
2. Substitute these values into the discriminant formula:
\[ D = (1)^2 - 4(a)(a) \] \[ D = 1 - 4a^2 \]
Step 4: Final Answer:
The discriminant is \(1 - 4a^2\).