+817 Find the smallest integer $c$ such that the domain of the function $f(x)=\frac{x^2+1}{x^2-x+c+3x^2-7x}$ is all real numbers.
+129881 The denominator cannot = 0
Simplifying the denominator we get
4x^2 -8x + c → this is an upward turning parabola
To have a domain of all real numbers, this parabola must lie above the x axis
So.....the discrimiant must be < 0 ....so....
(-8)^2 -4(4) ( c) < 0
64 - 16c < 0
64 < 16c
4 < c
So
c > 4
The smallest integer is 5
