Question

The sum of the roots of the quadratic equation $1 - 4x + 4x^2 = 0$ will be

• A. -2
• B. -1
• C. 1
• D. 2

Hint:

For a quadratic equation $ax^2 + bx + c = 0$: Sum of roots = $-\dfrac{b}{a}$, Product of roots = $\dfrac{c}{a}$.

Answer 1

The Correct Option is D

Step 1: Write in standard form.
\[ 4x^2 - 4x + 1 = 0 \] So, \(a = 4, b = -4, c = 1\). Step 2: Formula for sum of roots.
\[ \text{Sum of roots} = -\dfrac{b}{a} = -\dfrac{-4}{4} = 1 \] Wait, recheck original equation: \(1 - 4x + 4x^2 = 0\). This rearranges to \(4x^2 - 4x + 1 = 0\), giving sum \(=\dfrac{4}{4}=1\). So the correct answer is (C) 1. Step 3: Conclusion.
Hence, the sum of the roots is \(1\).