Find-the-values-of-k-if-x-2-3x-4-5x-k-may-be-capable-of-taking-on-all-values-when-x-is-real-

Question Number 33838 by NECx last updated on 25/Apr/18

F i n d t h e v a l u e s o f k i f \frac{x^{2} + 3 x - 4}{5 x - k}

m a y b e c a p a b l e o f t a k i n g o n a l l

v a l u e s w h e n x i s r e a l .

Answered by MJS last updated on 26/Apr/18

we have to get rid of the square \dots

\frac{1}{5} \times \frac{(x + 4) (x - 1)}{x - \frac{k}{5}}

- \frac{k}{5} = 4 \lor - \frac{k}{5} = - 1

k = - 20 \lor k = 5

\frac{x^{2} + 3 x - 4}{5 x - k} = \frac{1}{5} (x - 1) \lor \frac{x^{2} + 3 x - 4}{5 x - k} = \frac{1}{5} (x + 4)

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