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CAT Quantitative Aptitude Questions | CAT Algebra - Linear Equations; Quadratic Equations

CAT Questions | Algebra | Quadratic Equations - Counting

The question is about finding possible values of the constant in a Quadratic Equation. We need to find out the no. of values 'k' can take when the given quadratic equations has real roots. Framing and solving equations is an integral part of Linear Equations and Quadratic Equations. Get as much practice as you can in these two topics because the benefits of being good at framing equations will be useful in other concepts.

Question 5: x2 - 9x + |k| = 0 has real roots. How many integer values can 'k' take?

  1. 40
  2. 21
  3. 20
  4. 41

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Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Quadratic Equations: Counting question with modulus also thrown in. Worry about all those negative possibilities as well.

Discriminant, D = 81 – 4|k|
If roots are real, D > 0
81 – 4|k| > 0
4|k| < 81
|k| < 20.25

Hence, –20.25 < k < 20.25
The integer values that k can take are –20, –19, –18 … 0 … 18, 19 and 20.

41 different values (Remember to include 0.)

The question is "x2 - 9x + |k| = 0 has real roots. How many integer values can 'k' take?"

Hence the answer is "41"

Choice D is the correct answer.


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