Choose the correct conclusion about the nature of the roots of the equation \(3x^2-4\sqrt{3}x+5=0\).
Answer and explanation
Correct answer: No real roots \((\Delta=-12)\)
Here, \(a=3\), \(b=-4\sqrt{3}\), and \(c=5\). Therefore, the discriminant is \(\Delta=b^2-4ac=(-4\sqrt{3})^2-4(3)(5)=48-60=-12\). Since \(\Delta<0\), the equation has no real roots. Option B is incorrect because equal real roots require \(\Delta=0\). Exam tip: For a quadratic equation, a negative discriminant always indicates that no real roots exist.
Frequently asked questions
What is the correct answer to this question?
No real roots \((\Delta=-12)\)
Why is this the correct answer?
Here, \(a=3\), \(b=-4\sqrt{3}\), and \(c=5\). Therefore, the discriminant is \(\Delta=b^2-4ac=(-4\sqrt{3})^2-4(3)(5)=48-60=-12\). Since \(\Delta<0\), the equation has no real roots. Option B is incorrect because equal real roots require \(\Delta=0\). Exam tip: For a quadratic equation, a negative discriminant always indicates that no real roots exist.
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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