What is the nature of the roots of the quadratic equation \(3x^2-2\sqrt{6}x+2=0\)?
Answer and explanation
Correct answer: Two real and equal roots \(D=0\)
Here, \(a=3\), \(b=-2\sqrt{6}\), and \(c=2\). Therefore, the discriminant is \(D=b^2-4ac=(-2\sqrt{6})^2-4(3)(2)=24-24=0\). When \(D=0\), the quadratic equation has two real and equal roots. Hence, option A is correct. Exam tip: \(D<0\) indicates no real roots, while \(D=0\) specifically indicates equal real roots.
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, \(a=3\), \(b=-2\sqrt{6}\), and \(c=2\). Therefore, the discriminant is \(D=b^2-4ac=(-2\sqrt{6})^2-4(3)(2)=24-24=0\). When \(D=0\), the quadratic equation has two real and equal roots. Hence, option A is correct. Exam tip: \(D<0\) indicates no real roots, while \(D=0\) specifically indicates equal real roots.
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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