Choose the correct conclusion about the nature of the roots of \(x^2-2\sqrt{5}x+6=0\).
Answer and explanation
Correct answer: No real roots \(\Delta=-4\)
For the given quadratic equation, \(a=1\), \(b=-2\sqrt{5}\), and \(c=6\). Thus, the discriminant is \(\Delta=b^2-4ac=(-2\sqrt{5})^2-4(1)(6)=20-24=-4\). Since \(\Delta<0\), the equation has no real roots, so option A is correct. Exam tip: a negative discriminant means the roots are non-real; equal real roots occur only when \(\Delta=0\).
Frequently asked questions
What is the correct answer to this question?
No real roots \(\Delta=-4\)
Why is this the correct answer?
For the given quadratic equation, \(a=1\), \(b=-2\sqrt{5}\), and \(c=6\). Thus, the discriminant is \(\Delta=b^2-4ac=(-2\sqrt{5})^2-4(1)(6)=20-24=-4\). Since \(\Delta<0\), the equation has no real roots, so option A is correct. Exam tip: a negative discriminant means the roots are non-real; equal real roots occur only when \(\Delta=0\).
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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