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Find all values of \(k\) so that the domain of

\(b(x) = \frac{kx^2 + 2x - 5}{-5x^2 + 2x + k}\)

is the set of all real numbers.

 Feb 19, 2021
 #1
avatar+287 
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The numerator does not matter in this case; only if the denominator is zero for some real number, the domain will not be set for all real numbers.

To prevent the denominator from having real roots, the discriminant must be negative, which means \(2^2-4\cdot-5\cdot k = 4+20k\) is negative.

That will only happen if \(\boxed{k<-\frac{1}{5}}\).

 Feb 19, 2021
 #2
avatar+74 
+1

It's correct, thanks!!cool

pizzaisawesome972  Feb 20, 2021

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