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Subjects
Class 10MathematicsQuadratic EquationsNature of RootsHardLevel 38
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What is the nature of roots of (x^2-2(a-5)x+a^2-10a+21=0)?

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Answer and explanation

Correct answer: Always real and distinct

Here (D=4(a-5)^2-4(a^2-10a+21)=16>0). Therefore the roots are real and distinct for every real (a).

Related tags

Quadratic EquationsConstant DiscriminantReal Distinct Roots

Frequently asked questions

What is the correct answer to this question?

Always real and distinct

Why is this the correct answer?

Here (D=4(a-5)^2-4(a^2-10a+21)=16>0). Therefore the roots are real and distinct for every real (a).

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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  1. 1If the discriminant D > 0 for a quadratic equation, what will be the nature of its roots?
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  3. 3What is the nature of the roots of x² + 6x + 9 = 0?
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  7. 7Which equation has discriminant −15?
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