What is the nature of the roots of \\(x^2-2(3+\sqrt{2})x+(17+12\sqrt{2})=0\\)?
Answer and explanation
Correct answer: No real roots
Here, \\(a=1\\), \\(b=-2(3+\sqrt{2})\\), and \\(c=17+12\sqrt{2}\\). Therefore, the discriminant is \\(D=b^2-4ac=4(3+\sqrt{2})^2-4(17+12\sqrt{2})=-24(1+\sqrt{2})<0\\). Hence, the quadratic has no real roots; its roots are a pair of complex conjugates. Remember that real and equal roots occur only when \\(D=0\\).
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(3+\sqrt{2})\\), and \\(c=17+12\sqrt{2}\\). Therefore, the discriminant is \\(D=b^2-4ac=4(3+\sqrt{2})^2-4(17+12\sqrt{2})=-24(1+\sqrt{2})<0\\). Hence, the quadratic has no real roots; its roots are a pair of complex conjugates. Remember that real and equal roots occur only when \\(D=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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