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Class 10MathematicsQuadratic EquationsRoots of a Quadratic EquationMediumLevel 33
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What is the repeated root of the equation \(25x^2-10x+1=0\)?

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Answer and explanation

Correct answer: \(\frac{1}{5}\)

The equation can be factorised as \(25x^2-10x+1=(5x-1)^2=0\). Thus, \(5x-1=0\), giving \(x=\frac{1}{5}\). This is the repeated root. In an exam, identifying a perfect square or checking that the discriminant is zero is the quickest approach.

Related tags

Quadratic EquationsRepeated RootRootsPerfect SquareDiscriminant

Frequently asked questions

What is the correct answer to this question?

\(\frac{1}{5}\)

Why is this the correct answer?

The equation can be factorised as \(25x^2-10x+1=(5x-1)^2=0\). Thus, \(5x-1=0\), giving \(x=\frac{1}{5}\). This is the repeated root. In an exam, identifying a perfect square or checking that the discriminant is zero is the quickest approach.

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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