For the equation \(5x^2+2x+1=0\), what is the sign of the discriminant \(D\) and the nature of its roots?
Answer and explanation
Correct answer: D < 0, no real roots
Here, \(a=5\), \(b=2\), and \(c=1\). Thus, the discriminant is \(D=b^2-4ac=2^2-4(5)(1)=4-20=-16\), so \(D<0\). A negative discriminant means that the quadratic equation has no real roots; its roots are complex conjugates. Option B would be correct only if \(D=0\). Exam tip: remember that \(D<0\), \(D=0\), and \(D>0\) correspond respectively to no real roots, equal real roots, and distinct real roots.
Frequently asked questions
What is the correct answer to this question?
D < 0, no real roots
Why is this the correct answer?
Here, \(a=5\), \(b=2\), and \(c=1\). Thus, the discriminant is \(D=b^2-4ac=2^2-4(5)(1)=4-20=-16\), so \(D<0\). A negative discriminant means that the quadratic equation has no real roots; its roots are complex conjugates. Option B would be correct only if \(D=0\). Exam tip: remember that \(D<0\), \(D=0\), and \(D>0\) correspond respectively to no real roots, equal real roots, and distinct 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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