What is the correct nature of the roots of \(6x^2-x-2=0\)?
Answer and explanation
Correct answer: Two real, rational and distinct roots \(D=49\)
Here, \(a=6, b=-1, c=-2\), so the discriminant is \(D=b^2-4ac=(-1)^2-4(6)(-2)=49\). Since \(D\) is positive and a perfect square, the roots are real, rational, and distinct. Option B would require \(D=0\), while the value \(D=7\) in option D is incorrect. Exam tip: If \(D>0\) and is a perfect square, the roots are rational and distinct.
Frequently asked questions
What is the correct answer to this question?
Two real, rational and distinct roots \(D=49\)
Why is this the correct answer?
Here, \(a=6, b=-1, c=-2\), so the discriminant is \(D=b^2-4ac=(-1)^2-4(6)(-2)=49\). Since \(D\) is positive and a perfect square, the roots are real, rational, and distinct. Option B would require \(D=0\), while the value \(D=7\) in option D is incorrect. Exam tip: If \(D>0\) and is a perfect square, the roots are rational and distinct.
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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