What is the smallest integer value of $c$ such that the function $f(x)=\frac{x^2+1}{x^2-x+c}$ has a domain of all real numbers?

Guest Aug 2, 2022

#2**0 **

For the function to have a domain of all real numbers, the denominator must ave imaginary solutions.

For an equation to have imaginary solutions, the discriminant(b^2 - 4ac) must be negative.

So, we have the equation \(1 - 4c < 0\). The smallest possible integer that works is \(\color{brown}\boxed{1}\)

BuilderBoi Aug 3, 2022

#2**0 **

Best Answer

For the function to have a domain of all real numbers, the denominator must ave imaginary solutions.

For an equation to have imaginary solutions, the discriminant(b^2 - 4ac) must be negative.

So, we have the equation \(1 - 4c < 0\). The smallest possible integer that works is \(\color{brown}\boxed{1}\)

BuilderBoi Aug 3, 2022