Question

Find k such that 16x2 – 8 /3x+k=0 has a repeated real solution.

Answer 1

k =
`(1)/(9)`

Explanation:

Using the discriminant

Δ = b² - 4ac

For a repeated real solution then

b² - 4ac = 0

Given

16x² -
`(8)/(3)` x + k = 0

with a = 16, b = -
`(8)/(3)` , c = k

(-
`(8)/(3)` )² - ( 4 × 16 × k) = 0

`(64)/(9)` - 64k = 0 ( subtract
`(64)/(9)` from both sides )

- 64k = -
`(64)/(9)` ( divide both sides by - 64 )

k =
`(1)/(9)`