Which is the nature of roots in the equation (9x^2-6x+1=0)?
Answer and explanation
Correct answer: Real and equal
Here, \(a=9\), \(b=-6\), and \(c=1\). The discriminant is \(D=b^2-4ac=(-6)^2-4(9)(1)=36-36=0\). When \(D=0\), a quadratic equation has two real and equal roots. In fact, \((3x-1)^2=0\), so both roots are \(x=\frac{1}{3}\). “Two positive and distinct” is incorrect because the root is positive but repeated, not distinct. Exam tip: determine the nature of roots by checking the sign of the discriminant first.
Frequently asked questions
What is the correct answer to this question?
Real and equal
Why is this the correct answer?
Here, \(a=9\), \(b=-6\), and \(c=1\). The discriminant is \(D=b^2-4ac=(-6)^2-4(9)(1)=36-36=0\). When \(D=0\), a quadratic equation has two real and equal roots. In fact, \((3x-1)^2=0\), so both roots are \(x=\frac{1}{3}\). “Two positive and distinct” is incorrect because the root is positive but repeated, not distinct. Exam tip: determine the nature of roots by checking the sign of the discriminant first.
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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