#### Question

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

4x^{2} + kx + 9 = 0

#### Solution

The given quadric equation is 4x^{2} + 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 = b^{2} - 4ac

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

= (k)^{2} - 4 x (4) x (9)

= k^{2} - 144

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

Thus,

k^{2} - 144 = 0

k^{2} = 144

`k=sqrt144`

k = ± 12

Therefore, the value of k = ± 12.

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#### APPEARS IN

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.