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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

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 #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
avatar+2270 
+2
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

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