What is the nature of the roots of the equation \(x^2+2(1-\sqrt{3})x+4=0\)?
Answer and explanation
Correct answer: No real roots
Here, \(a=1\), \(b=2(1-\sqrt{3})\), and \(c=4\). Therefore, the discriminant is \(D=b^2-4ac=4(1-\sqrt{3})^2-16=-8\sqrt{3}<0\). Hence, the equation has no real roots. Option B would be correct only if \(D=0\). Exam tip: For a quadratic equation, \(D<0\) indicates non-real, or complex, roots.
Frequently asked questions
What is the correct answer to this question?
No real roots
Why is this the correct answer?
Here, \(a=1\), \(b=2(1-\sqrt{3})\), and \(c=4\). Therefore, the discriminant is \(D=b^2-4ac=4(1-\sqrt{3})^2-16=-8\sqrt{3}<0\). Hence, the equation has no real roots. Option B would be correct only if \(D=0\). Exam tip: For a quadratic equation, \(D<0\) indicates non-real, or complex, 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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