Find the values of k if ((x^2 +3x−4)/(5x−k)) may be capable of taking on all values when x is real.


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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

	$we have to get rid of the square . . .$ $\frac{1}{5} \times \frac{(x + 4) (x - 1)}{x - \frac{k}{5}}$ $- \frac{k}{5} = 4 \lor - \frac{k}{5} = - 1$ $k = - 20 \lor k = 5$ $\frac{x^{2} + 3 x - 4}{5 x - k} = \frac{1}{5} (x - 1) \lor \frac{x^{2} + 3 x - 4}{5 x - k} = \frac{1}{5} (x + 4)$
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