#### Question

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

9x^{2} - 24x + k = 0

#### Solution

The given quadric equation is 9x^{2} - 24x + k = 0, and roots are real and equal

Then find the value of *k.*

Here, a = 9, b = -24 and c = k

As we know that D = b^{2} - 4ac

Putting the value of a = 9, b = -24 and c = k

= (-24)^{2} - 4 x (9) x (k)

= 576 - 36k

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

Thus,

576 - 36k = 0

36k = 576

k = 576/36

k = 16

Therefore, the value of k = 16.

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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: 9x2 - 24x + K = 0 Concept: Nature of Roots.