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Class 10 Mathematics Quadratic Equations Nature of RootsExpertLevel 38

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If the discriminant of a quadratic equation is ( D=-(p-1)^2 ) and ( p\ne 1 ), what is the nature of its roots?

Answer and explanation

Correct answer: No real roots

Since ( p\ne 1 ), we have ( (p-1)^2>0 ). Therefore, ( D=-(p-1)^2<0 ). A negative discriminant means that the quadratic equation has no real roots, so option A is correct. Exam tip: ( D=0 ) gives real and equal roots, while ( D>0 ) gives real and distinct roots.

Related tags

Quadratic-Equations Discriminant Nature-Of-Roots No-Real-Roots

Frequently asked questions

What is the correct answer to this question?

No real roots

Why is this the correct answer?

Since ( p\ne 1 ), we have ( (p-1)^2>0 ). Therefore, ( D=-(p-1)^2<0 ). A negative discriminant means that the quadratic equation has no real roots, so option A is correct. Exam tip: ( D=0 ) gives real and equal roots, while ( D>0 ) gives real and distinct 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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