What is the repeated root of the equation \(16x^2-8x+1=0\)?
Answer and explanation
Correct answer: \(\frac{1}{4}\)
The equation \(16x^2-8x+1=0\) can be written as \((4x-1)^2=0\). Hence, \(4x-1=0\), giving the repeated root \(x=\frac{1}{4}\). Exam tip: when a quadratic is a perfect square, its single root is repeated twice; do not confuse it with the coefficient 4 in the factor.
Frequently asked questions
What is the correct answer to this question?
\(\frac{1}{4}\)
Why is this the correct answer?
The equation \(16x^2-8x+1=0\) can be written as \((4x-1)^2=0\). Hence, \(4x-1=0\), giving the repeated root \(x=\frac{1}{4}\). Exam tip: when a quadratic is a perfect square, its single root is repeated twice; do not confuse it with the coefficient 4 in the factor.
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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