What are the two roots of the equation \(4x^2-4x+1=0\)?
Answer and explanation
Correct answer: \(\frac{1}{2},\frac{1}{2}\)
Since \(4x^2-4x+1=(2x-1)^2\), the equation gives \((2x-1)^2=0\), so \(2x-1=0\) and \(x=\frac{1}{2}\). Also, the discriminant \(D=b^2-4ac\) is zero, confirming that the two roots are equal. Therefore, both roots are \(\frac{1}{2},\frac{1}{2}\). Exam tip: A quadratic that is a perfect square, or has \(D=0\), has equal roots.
Frequently asked questions
What is the correct answer to this question?
\(\frac{1}{2},\frac{1}{2}\)
Why is this the correct answer?
Since \(4x^2-4x+1=(2x-1)^2\), the equation gives \((2x-1)^2=0\), so \(2x-1=0\) and \(x=\frac{1}{2}\). Also, the discriminant \(D=b^2-4ac\) is zero, confirming that the two roots are equal. Therefore, both roots are \(\frac{1}{2},\frac{1}{2}\). Exam tip: A quadratic that is a perfect square, or has \(D=0\), has equal roots.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Roots of a Quadratic Equation.
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