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What is the value of the equal root of the equation \(9x^2-6x+1=0\)?
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Answer and explanation
Correct answer: \(x=\frac{1}{3}\)
The equation can be factorised as \(9x^2-6x+1=(3x-1)^2\). Thus, \((3x-1)^2=0\), giving \(3x-1=0\) and the equal root \(x=\frac{1}{3}\). Exam tip: For equal roots, the discriminant \(D=b^2-4ac\) is zero.
Frequently asked questions
What is the correct answer to this question?
\(x=\frac{1}{3}\)
Why is this the correct answer?
The equation can be factorised as \(9x^2-6x+1=(3x-1)^2\). Thus, \((3x-1)^2=0\), giving \(3x-1=0\) and the equal root \(x=\frac{1}{3}\). Exam tip: For equal roots, the discriminant \(D=b^2-4ac\) is zero.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
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