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Class 10MathematicsQuadratic EquationsNature of RootsExpertLevel 39
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If \(p\) is any real number, what is the nature of the roots of the equation \(x^2+2px+(p^2+1)=0\)?

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Answer and explanation

Correct answer: no real roots

Here \(a=1, b=2p\), and \(c=p^2+1\). Thus \(\Delta=b^2-4ac=4p^2-4(p^2+1)=-4<0\), so there are no real roots. In exams, check the sign of the discriminant first.

Related tags

Quadratic EquationsNature Of RootsDiscriminantReal CoefficientsNon-Real Roots

Frequently asked questions

What is the correct answer to this question?

no real roots

Why is this the correct answer?

Here \(a=1, b=2p\), and \(c=p^2+1\). Thus \(\Delta=b^2-4ac=4p^2-4(p^2+1)=-4<0\), so there are no real roots. In exams, check the sign of the discriminant first.

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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