Question

Ifx2-3x - 4<0 then x lies in the interval​

Answer 1

Answer:

$x$ lies in the interval $(-1,4)$

Step-by-step explanation:

$x^2-3x-4$ is a parabola opening to the top, once the quadratic coefficient is positive. Then we just need to find its roots and the desired interval will be defined, as we can see in the graphic below. That happens because the parabola is "coming from positive infinity" and "going to positive infinity", then in order to have $x^2-3x-4<0$, it will need to pass through the x-axis twice (once to become negative, once to become positive and never negative again). So between these two moments, it will be negative.

Using the quadratic formula, we have $-1$ and $4$ as zeros of this parabola. Then $x \in (-1,4).$