Find $m$ such that $(m-1)x^{2}+(m-1)x+m-3<0$ I need to find $m$ real parameter such that $(m-1)x^{2}+(m-1)x+m-3<0$ for all real $x$.
My try: First condition $m-1<0$ so $m<1$
Second condition: the discriminant $<0$ from which I got $m\in(-\infty,1)\cup(\frac{11}{3},\infty)$
So when I intersectate the intervals I get $m\in(-\infty,1)$ which in my book is the wrong answer.
I need to chose from: A. m does not exist. B. $m\in(-\infty,1)\cup(\frac{11}{3},\infty)$ C. $m\in(-\infty,0)$ D.$m\in(-\infty,1)$ E.Another answer (The right answer is E.)
I miss something?

Your answer was almost correct; the assumption $m-1<0$ is not quite correct and should have been $\le$. Note $m=1$ works since you simply obtain $-2$ for all $x$, giving $(-\infty, 1]$.
