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In the Following Determine the Set of Values of K for Which the Given Quadratic Equation Has Real Roots: X2 - Kx + 9 = 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:

x2 - kx + 9 = 0

Solution

The given quadric equation is x2 - kx + 9 = 0, and roots are real.

Then find the value of k.

Here, a = 1, b = -k and c = 9

As we know that D = b2 - 4ac

Putting the value of a = 1, b = -k and c = 9

= (-k)2 - 4 x (1) x (9)

= k2 - 36

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

⇒ k2 - 36 ≥ 0

⇒ k2 ≥ 36

`rArrk>=sqrt36` Or `k<=sqrt36`

⇒ k ≥ 6 Or k ≤ -6

  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: X2 - Kx + 9 = 0 Concept: Nature of Roots.
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