For all equation `|x^(2) - 10x + 9| = kx`

Options

A. (a) If `k = 16`, then equation has exactly three solutions
B. (b) If `k = 4`, then equation has exactly three solutions
C. (c) if `k = -4`, then equation has exactly one solution
D. (d) if `k = -16`, then equation has exactly one solution

Answer

B, D

Explanation

for the given condition to be satisfied the value of `k` must lie between the siopes of line `OA` and `OB` for slope of line `OA`
`- (x^(2) - 10x + 9) = kx` must have equal roots
`rArr (k - 10)^(2) - 36 = 0 rArr k = 4, 16 rArr k = 4`
For slope of `OB x^(2) - 10x + 9 = kx` must have equal roots
`rArr (k + 10)^(2) - 36 = 0 rArr k = -4, -16`
`rArr k = -16`