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In the Following Determine the Set of Values of K for Which the Given Quadratic Equation Has Real Roots: 4x2 - 3kx + 1 = 0 - CBSE Class 10 - 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:

4x2 - 3kx + 1 = 0

Solution

The given quadric equation is 4x2 - 3kx + 1 = 0, and roots are real

Then find the value of k.

Here, a = 4, b = -3k and c = 1

As we know that D = b2 - 4ac

Putting the value of a = 4, b = -3k and c = 1

= (-3k)2 - 4 x (4) x (1)

= 9k2 - 16

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

⇒ 9k2 - 16 ≥ 0

⇒ 9k2 ≥ 16

⇒ k2 ≥ 16/9

`rArrk>=sqrt(16/9)` or `k<=-sqrt(16/9)`

⇒ k ≥ 4/3 Or k ≤ -4/3

  Is there an error in this question or solution?

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Solution In the Following Determine the Set of Values of K for Which the Given Quadratic Equation Has Real Roots: 4x2 - 3kx + 1 = 0 Concept: Nature of Roots.
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