Choose the correct statement about the nature of the roots of \(2x^2-5x+2=0\).
Answer and explanation
Correct answer: Two real, rational, and distinct roots \(D=9\)
For the given quadratic equation, \(a=2\), \(b=-5\), and \(c=2\). Therefore, the discriminant is \(D=b^2-4ac=(-5)^2-4(2)(2)=25-16=9\). Since \(D\) is positive and a perfect square, the roots are real, rational, and distinct. Option B is incorrect because a positive discriminant gives irrational roots only when it is not a perfect square. Exam tip: \(D>0\) indicates distinct real roots, while a perfect-square discriminant indicates that the roots are rational.
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What is the correct answer to this question?
Two real, rational, and distinct roots \(D=9\)
Why is this the correct answer?
For the given quadratic equation, \(a=2\), \(b=-5\), and \(c=2\). Therefore, the discriminant is \(D=b^2-4ac=(-5)^2-4(2)(2)=25-16=9\). Since \(D\) is positive and a perfect square, the roots are real, rational, and distinct. Option B is incorrect because a positive discriminant gives irrational roots only when it is not a perfect square. Exam tip: \(D>0\) indicates distinct real roots, while a perfect-square discriminant indicates that the roots are rational.
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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