Question

Find the value of k for which the roots of 9x^2+8kx+16=0are real and equal

Answer 1

roots are real and equal

D=0

b^2-4ac=0

(8k)^2-4×9×16=0

64k^2-576=0

64k^2=576

k^2=576/64

k^2=9

$k = \sqrt{9}$

k=3

Answer 2

Given Equation,

9x² + 8Kx + 16 = 0

The above equation has real and equal roots i.e,discriminant of the equation is equal to zero

Comparing with ax² + bx + c = 0,

a = 9,b = 8K and c = 16

Now,

Discriminant = 0

》 b² - 4ac = 0

》 (8K)² = 4(9)(16)

》 64K² = 576

》 K² = 576/64

》 K² = 9

》 K = 3

For K = 3,the given equation has real and equal roots