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# The Values of K for Which the Quadratic Equation 16 X 2 + 4 K X + 9 = 0 Has Real and Equal Roots Are - Mathematics

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#### Question

The values of k for which the quadratic equation  $16 x^2 + 4kx + 9 = 0$  has real and equal roots are

##### Options
• $6, - \frac{1}{6}$

• 36, −36

•  6, −6

• $\frac{3}{4}, - \frac{3}{4}$

#### Solution

The given quadratic equation  $16 x^2 + 4kx + 9 = 0$

has equal roots.

Here,

$a = 16, b = 4k \text { and } c = 9$ .

As we know that

$D = b^2 - 4ac$
Putting the values of  $a = 16, b = 4k \text { and } c = 9$.

$D = \left( 4k \right)^2 - 4\left( 16 \right)\left( 9 \right)$

$= 16 k^2 - 576$

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

Thus,

$16 k^2 - 576 = 0$

$\Rightarrow k^2 - 36 = 0$

$\Rightarrow (k + 6)(k - 6) = 0$

$\Rightarrow k + 6 = 0 \text { or } k - 6 = 0$

$\Rightarrow k = - 6 \text { or } k = 6$

Therefore, the value of k is 6, −6.

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