Choose the correct statement about the nature of the roots of the equation \(2x^2+x+3=0\).
Answer and explanation
Correct answer: No real roots \(D=-23\)
Here, \(a=2\), \(b=1\), and \(c=3\). Therefore, the discriminant is \(D=b^2-4ac=1^2-4(2)(3)=-23\). Since \(D<0\), the quadratic equation has no real roots. Options B and C are incorrect because they correspond to \(D=0\) and \(D>0\), respectively. Exam tip: To determine the nature of the roots, first check the sign of the discriminant.
Frequently asked questions
What is the correct answer to this question?
No real roots \(D=-23\)
Why is this the correct answer?
Here, \(a=2\), \(b=1\), and \(c=3\). Therefore, the discriminant is \(D=b^2-4ac=1^2-4(2)(3)=-23\). Since \(D<0\), the quadratic equation has no real roots. Options B and C are incorrect because they correspond to \(D=0\) and \(D>0\), respectively. Exam tip: To determine the nature of the roots, first check the sign of the discriminant.
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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