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# help

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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?

Aug 2, 2022

#2
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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 $$\color{brown}\boxed{1}$$

Aug 3, 2022

#1
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The smallest integer that works is 4.

Aug 2, 2022
#2
+2448
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