What is the nature of the roots of the quadratic equation \(2x^2-6\sqrt{2}x+9=0\)?
Answer and explanation
Correct answer: Two real and equal, \(\Delta=0\)
Here, \(a=2\), \(b=-6\sqrt{2}\), and \(c=9\). Therefore, the discriminant is \(\Delta=b^2-4ac=(-6\sqrt{2})^2-4(2)(9)=72-72=0\). When \(\Delta=0\), the quadratic equation has two real and equal roots. In fact, the repeated root is \(x=\frac{3\sqrt{2}}{2}\). Hence, option A is correct; options B and D require a positive discriminant, whereas the discriminant here is zero. Exam tip: To determine the nature of roots, first check the sign of \(\Delta\).
Frequently asked questions
What is the correct answer to this question?
Two real and equal, \(\Delta=0\)
Why is this the correct answer?
Here, \(a=2\), \(b=-6\sqrt{2}\), and \(c=9\). Therefore, the discriminant is \(\Delta=b^2-4ac=(-6\sqrt{2})^2-4(2)(9)=72-72=0\). When \(\Delta=0\), the quadratic equation has two real and equal roots. In fact, the repeated root is \(x=\frac{3\sqrt{2}}{2}\). Hence, option A is correct; options B and D require a positive discriminant, whereas the discriminant here is zero. Exam tip: To determine the nature of roots, first check the sign of \(\Delta\).
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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