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In the Following Determine the Set of Values of K for Which the Given Quadratic Equation Has Real Roots: 2x2 - 5x - K = 0 - Mathematics

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Question

In the following determine the set of values of k for which the given quadratic equation has real roots:

2x2 - 5x - k = 0

Solution

The given quadric equation is 2x2 - 5x - k = 0, and roots are real

Then find the value of k.

Here, a = 2, b = -5 and c = k

As we know that D = b2 - 4ac

Putting the value of a = 2, b = -5 and c = k

= (-5)2 - 4 x (2) x (-k)

= 25 + 8k

The given equation will have real roots, if D ≥ 0

25 + 8k ≥ 0

8k ≥ -25

k ≥ -25/8

Therefore, the value of k ≥ -25/8.

  Is there an error in this question or solution?
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APPEARS IN

 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.6 | Q: 3.3 | Page no. 42
 RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 4: Quadratic Equations
Ex. 4.6 | Q: 3.3 | Page no. 42
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Solution In the Following Determine the Set of Values of K for Which the Given Quadratic Equation Has Real Roots: 2x2 - 5x - K = 0 Concept: Nature of Roots.
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