What is the nature of the roots of the equation \\(7x^2-2\\sqrt{21}x+3=0\\)?
Answer and explanation
Correct answer: Two real and equal roots (\(D=0\))
Here, a=7, b=-2\(\sqrt{21}\), and c=3. Therefore, the discriminant is \(D=b^2-4ac=(-2\sqrt{21})^2-4(7)(3)=84-84=0\). Hence, the roots are real and equal. In fact, the repeated root is \(x=\frac{\sqrt{21}}{7}\). Option D incorrectly treats 84, which is only the value of \(b^2\), as the discriminant. Exam tip: \(D=0\) always indicates two equal real roots.
Frequently asked questions
What is the correct answer to this question?
Two real and equal roots (\(D=0\))
Why is this the correct answer?
Here, a=7, b=-2\(\sqrt{21}\), and c=3. Therefore, the discriminant is \(D=b^2-4ac=(-2\sqrt{21})^2-4(7)(3)=84-84=0\). Hence, the roots are real and equal. In fact, the repeated root is \(x=\frac{\sqrt{21}}{7}\). Option D incorrectly treats 84, which is only the value of \(b^2\), as the discriminant. Exam tip: \(D=0\) always indicates two equal real roots.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Nature of Roots.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
