+118723 $$x^2-3x-10<0$$
The easiest way to do these is to think of a the parabola
$$y=x^2-3x-10\\$$
The above inequality will be true when y is negative. i.e. the parabola is under the x axis.
This is a concave up parabola because the coefficient of x^2 is positive
So we will need to solve
$$\\x^2-3x-10=0\\
(x-5)(x+2)=0\\
x=5,\;\;x=-2\\$$
since the paraola is concave up, the bit under the x axis is between these two roots.
so
$$\\x^2-3x-10<0\\
When\;\;-2
+118723 $$x^2-3x-10<0$$
The easiest way to do these is to think of a the parabola
$$y=x^2-3x-10\\$$
The above inequality will be true when y is negative. i.e. the parabola is under the x axis.
This is a concave up parabola because the coefficient of x^2 is positive
So we will need to solve
$$\\x^2-3x-10=0\\
(x-5)(x+2)=0\\
x=5,\;\;x=-2\\$$
since the paraola is concave up, the bit under the x axis is between these two roots.
so
$$\\x^2-3x-10<0\\
When\;\;-2
