What is the nature of the roots of the equation \\(5x^2-2\\sqrt{30}x+6=0\\)?
Answer and explanation
Correct answer: Two real and equal roots \\(\\Delta=0\\)
Here, \\(a=5\\), \\(b=-2\\sqrt{30}\\), and \\(c=6\\). Therefore, the discriminant is \\(\\Delta=b^2-4ac=(-2\\sqrt{30})^2-4(5)(6)=120-120=0\\). Hence, the roots are real and equal. Option D is incorrect because \\(\\Delta>0\\) would indicate distinct roots. Exam tip: For a quadratic equation, \\(\\Delta=0\\) always means two equal real roots.
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What is the correct answer to this question?
Two real and equal roots \\(\\Delta=0\\)
Why is this the correct answer?
Here, \\(a=5\\), \\(b=-2\\sqrt{30}\\), and \\(c=6\\). Therefore, the discriminant is \\(\\Delta=b^2-4ac=(-2\\sqrt{30})^2-4(5)(6)=120-120=0\\). Hence, the roots are real and equal. Option D is incorrect because \\(\\Delta>0\\) would indicate distinct roots. Exam tip: For a quadratic equation, \\(\\Delta=0\\) always means 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.
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