Question

find the value of k for which equation 9x^2+8xk+8=0 has equal roots.

Answer 1

for equal roots
discriminant must be equal to zero
D = b²-4ac must be zero
here b = 8k , a= 9 and c = 8
so (8k)²-4×9×8= 0
64k²= 288
k² = 9/2
k = 3/√2
k = 2.1

Answer 2

Given,

An equation 9x²+8xk+8=0.

To find,

To find the value of k for which equation 9x²+8xk+8=0 has equal roots.

Solution,

For the quadratic equation having equal roots, their Discriminant is always equal to zero.

Suppose an equation is of the form ax²+bx+c=0 where a, b and c are constant.

Discriminant (D) is calculated by D = b²-4ac.

In the given question,

a = 9 b = 8k c =8

Hence D = (8k)²-4(9)(8) = 0

⇒   D = 81k²- 288 = 0

⇒   81k² = 288

⇒   k² = 288/81

⇒   k² = 96/27

⇒   k =+-(4√6) / (3√3)

⇒   k = +4√2/3 and -4√2/3.

Hence the value of k for which equation 9x²+8xk+8=0 has equal roots are k = +4√2/3 and -4√2/3.