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# Find the Values Of K For Which the Roots Are Real and Equal in Each of the Following Equation: 4x2 + Kx + 9 = 0 - CBSE Class 10 - Mathematics

#### Question

Find the values of k for which the roots are real and equal in each of the following equation:

4x2 + kx + 9 = 0

#### Solution

The given quadric equation is 4x2 + kx + 9 = 0, and roots are real and equal

Then find the value of k.

Here, a = 4, b = k and c = 9

As we know that D = b2 - 4ac

Putting the value of a = 4, b = k and c = 9

= (k)2 - 4 x (4) x (9)

= k2 - 144

The given equation will have real and equal roots, if D = 0

Thus,

k2 - 144 = 0

k2 = 144

k=sqrt144

k = ± 12

Therefore, the value of k = ± 12.

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Solution Find the Values Of K For Which the Roots Are Real and Equal in Each of the Following Equation: 4x2 + Kx + 9 = 0 Concept: Nature of Roots.
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