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Class 10MathematicsQuadratic EquationsNature of RootsExpertLevel 37
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If (a\neq0) and (b^2-4ac) is a positive perfect square in (ax^2+bx+c=0), what is the most accurate nature of the roots?

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Answer and explanation

Correct answer: Two real rational and distinct

A positive perfect-square discriminant gives two distinct rational real roots. In exams check not only (D>0) but also whether (D) is a perfect square.

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Quadratic-EquationsNature-Of-RootsExpert

Frequently asked questions

What is the correct answer to this question?

Two real rational and distinct

Why is this the correct answer?

A positive perfect-square discriminant gives two distinct rational real roots. In exams check not only (D>0) but also whether (D) is a perfect square.

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?
  2. 2What is the discriminant D of 4x² + 4x + 1 = 0?
  3. 3What is the nature of the roots of x² + 6x + 9 = 0?
  4. 4If the roots of x² − 6x + k = 0 are equal, what is k?
  5. 5If the discriminant D = 49, what is the nature of the roots of the quadratic equation?
  6. 6If (D=64), what will be the nature of roots of the quadratic equation?
  7. 7Which equation has discriminant −15?
  8. 8If one root of x² + ax + 12 = 0 is 3, what are the other root and a?
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  10. 10What is the nature of the roots of 4x² − 12x + 9 = 0?
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