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Class 10MathematicsQuadratic EquationsRoots of a Quadratic EquationMediumLevel 31
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What is the repeated root of the equation \(9x^2-6x+1=0\)?

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Answer and explanation

Correct answer: \(\frac{1}{3}\)

The equation can be factorised as \(9x^2-6x+1=(3x-1)^2\). Thus, \(3x-1=0\), giving \(x=\frac{1}{3}\), which is the repeated root. Option B has the incorrect sign. Exam tip: the roots of a quadratic equation are equal when its discriminant \(D\) is zero.

Related tags

Quadratic EquationsRepeated RootsRootsDiscriminantFactorisation

Frequently asked questions

What is the correct answer to this question?

\(\frac{1}{3}\)

Why is this the correct answer?

The equation can be factorised as \(9x^2-6x+1=(3x-1)^2\). Thus, \(3x-1=0\), giving \(x=\frac{1}{3}\), which is the repeated root. Option B has the incorrect sign. Exam tip: the roots of a quadratic equation are equal when its discriminant \(D\) is zero.

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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