What are the roots of the equation \(9x^2-27x=0\)?
Answer and explanation
Correct answer: \(x=0, 3\)
Factoring the equation gives \(9x^2-27x=9x(x-3)=0\). By the zero-product rule, \(x=0\) or \(x-3=0\), which gives \(x=3\). Therefore, the roots are \(0\) and \(3\). Option B is incorrect because the second root is positive \(3\), not \(-3\). In an exam, factor out the common term first and then apply the zero-product rule.
Frequently asked questions
What is the correct answer to this question?
\(x=0, 3\)
Why is this the correct answer?
Factoring the equation gives \(9x^2-27x=9x(x-3)=0\). By the zero-product rule, \(x=0\) or \(x-3=0\), which gives \(x=3\). Therefore, the roots are \(0\) and \(3\). Option B is incorrect because the second root is positive \(3\), not \(-3\). In an exam, factor out the common term first and then apply the zero-product rule.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Methods of Solving Quadratic Equations.
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