Question

please solve this question...........​

Answer 1

Given Equation,

9x² + 8kx + 16 = 0

On comparing the given equation with the standard form (i.e., ax² + bx + c = 0 ) of we get,

a = 9, b = 8k, c = 16

For Real and Equal roots, value of discriminant must be equal to 0.

Discriminant, D = b² - 4ac

☛ D = 0

☛ b² - 4ac = 0

☛ b² = 4ac

☛ (8k)² = 4 × 9 × 16

☛ (8k)² = 576

Taking square root both sides,

☛ 8k = 24

☛ k = 3

Hence, For Equal and Real roots value of k must be 3.

Answer 2

k=3

Given :

The quadratic equation

$9x {}^{2} + 8kx + 16 = 0$

has equal and real roots

$\huge{\mathcal{\orange{\underline{Answer}}}}$

Condition for equal roots :

$b {}^{2} - 4ac = 0$

b = 8k

c = 16

a = 9

$(8k) {}^{2} - 4(9)(16) = 0 \\ 64k {}^{2} - 576 = 0 \\ 64k {}^{2} = 576 \\ k {}^{2} = \frac{576}{64} \\ k {}^{2} = 9 \\ k = \sqrt{9}$

$\huge{\mathcal{\orange{\implies{\underline{k=3}}}}}$