What is the nature of the roots of the quadratic equation \(3x^2-6x+3=0\)?
Answer and explanation
Correct answer: Two real and equal roots \(D=0\)
Here, \(a=3\), \(b=-6\), and \(c=3\). Therefore, the discriminant is \(D=b^2-4ac=(-6)^2-4(3)(3)=36-36=0\). Hence, the roots are real and equal. In fact, the equation can be written as \(3(x-1)^2=0\), giving the repeated root \(x=1\). Option B is incorrect because its discriminant value is wrong. Exam tip: When \(D=0\), the roots are always real and equal.
Frequently asked questions
What is the correct answer to this question?
Two real and equal roots \(D=0\)
Why is this the correct answer?
Here, \(a=3\), \(b=-6\), and \(c=3\). Therefore, the discriminant is \(D=b^2-4ac=(-6)^2-4(3)(3)=36-36=0\). Hence, the roots are real and equal. In fact, the equation can be written as \(3(x-1)^2=0\), giving the repeated root \(x=1\). Option B is incorrect because its discriminant value is wrong. Exam tip: When \(D=0\), the roots are always real and equal.
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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