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Class 10MathematicsQuadratic EquationsNature of RootsHard
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If (kx^2-6x+9=0) has real roots, what is the correct condition for (k)?

Answer and explanation

Correct answer: (k\le1) and (k\neq0)

For real roots, (D\ge0), so (36-36k\ge0) gives (k\le1). Also (k\neq0) is required because the equation must remain quadratic.

Related tags

Quadratic EquationsNature Of RootsReal Roots ConditionNature Of RootsQuadratic EquationsMathematicsClass 10 Mcq
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10 more MCQs
  1. 1If p(x) = 3x² − 12x + 6, what is the nature of its zeroes?
  2. 2What is the maximum number of real solutions possible for 2x² + 7x + 3 = 0?
  3. 3If the discriminant D > 0 for a quadratic equation, what will be the nature of its roots?
  4. 4What is the discriminant D of 4x² + 4x + 1 = 0?
  5. 5What is the nature of the roots of x² + 6x + 9 = 0?
  6. 6If the roots of x² − 6x + k = 0 are equal, what is k?
  7. 7If the discriminant D = 49, what is the nature of the roots of the quadratic equation?
  8. 8If D = 64, what will be the nature of the roots of the quadratic equation?
  9. 9Which equation has discriminant −15?
  10. 10If one root of x² + ax + 12 = 0 is 3, what are the other root and a?
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