Identify the nature of roots of (2x^2-7x+3=0).
Answer and explanation
Correct answer: Two real, rational and distinct roots
Here, \(a=2\), \(b=-7\), and \(c=3\). Therefore, the discriminant is \(D=b^2-4ac=(-7)^2-4(2)(3)=25\). Since \(D>0\), the roots are real and distinct; since \(D=25\) is a perfect square, they are also rational. In fact, the roots are \(3\) and \(\frac{1}{2}\). Hence, option A is correct. Exam tip: \(D>0\) indicates distinct real roots, while a perfect-square discriminant indicates rational roots.
Frequently asked questions
What is the correct answer to this question?
Two real, rational and distinct roots
Why is this the correct answer?
Here, \(a=2\), \(b=-7\), and \(c=3\). Therefore, the discriminant is \(D=b^2-4ac=(-7)^2-4(2)(3)=25\). Since \(D>0\), the roots are real and distinct; since \(D=25\) is a perfect square, they are also rational. In fact, the roots are \(3\) and \(\frac{1}{2}\). Hence, option A is correct. Exam tip: \(D>0\) indicates distinct real roots, while a perfect-square discriminant indicates rational 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.
