Question

If the equation \(ax^2-8x+4=0\) has equal roots then \(a=\) ____ .

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

The Correct Option is C

To solve the problem, we need to find the value of \( a \) such that the quadratic equation \( ax^2 - 8x + 4 = 0 \) has equal roots.

1. Understanding the Condition for Equal Roots:
For a quadratic equation \( ax^2 + bx + c = 0 \), the roots are equal if the discriminant is zero:

\( D = b^2 - 4ac = 0 \)

2. Identify the Coefficients:
Given equation: \( ax^2 - 8x + 4 = 0 \)
Here, \( a = a \), \( b = -8 \), and \( c = 4 \)

3. Apply the Discriminant Condition:
\[ (-8)^2 - 4a(4) = 0 \Rightarrow 64 - 16a = 0 \]

4. Solve for \( a \):
\[ 64 = 16a \Rightarrow a = \frac{64}{16} = 4 \]

Final Answer:
The value of \( a \) is \( 4 \) for the equation to have equal roots.