What is the nature of the roots of the equation \(4x^2-4\sqrt{3}x+3=0\)?
Answer and explanation
Correct answer: Two real and equal (\(D=0\))
Here, \(a=4\), \(b=-4\sqrt{3}\), and \(c=3\). Therefore, the discriminant is \(D=b^2-4ac=(-4\sqrt{3})^2-4(4)(3)=48-48=0\). When \(D=0\), the quadratic equation has two real and equal roots. In fact, the repeated root is \(x=\frac{\sqrt{3}}{2}\). Thus, option B is incorrect because the discriminant is not \(4\); it is \(0\). Exam tip: To determine the nature of the roots, first calculate \(D=b^2-4ac\).
Frequently asked questions
What is the correct answer to this question?
Two real and equal (\(D=0\))
Why is this the correct answer?
Here, \(a=4\), \(b=-4\sqrt{3}\), and \(c=3\). Therefore, the discriminant is \(D=b^2-4ac=(-4\sqrt{3})^2-4(4)(3)=48-48=0\). When \(D=0\), the quadratic equation has two real and equal roots. In fact, the repeated root is \(x=\frac{\sqrt{3}}{2}\). Thus, option B is incorrect because the discriminant is not \(4\); it is \(0\). Exam tip: To determine the nature of the roots, first calculate \(D=b^2-4ac\).
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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