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# For what values of \$b\$ is \$-2\$ not in the range of the function \$f(x)=x^2+bx+2\$? Express your answer in interval notation.

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For what values of b is -2 not in the range of the function f(x)=x^2+bx+2? Express your answer in interval notation.

Feb 8, 2019

### 4+0 Answers

#1
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Deleted ....

Feb 9, 2019
edited by ElectricPavlov  Feb 10, 2019
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We see that -2 is not in the range of f(x) = x^2 + bx + 2 if and only if the equation x^2 + bx + 2 = -2 has no real roots. We can re-write this equation as

x^2 + bx + 4 = 0. The discriminant of this quadratic is b^2 - 4 * 4 = b^2 - 16. The quadratic has no real roots if and only if the discriminant is negative, so ,  b^2 - 16 < 0 or b^2 < 16. The set of values that satisfy this inequality is (-4,4).

Also, this seems like an AoPS Alcumus Problem...

If it is... just letting you know that it's illegal to ask for alcumus problems, as AoPS has total rights over them.

Thanks!

Feb 10, 2019
edited by Guest  Feb 10, 2019
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Wait... it is an Alcumus Problem...

Don't post these problems, k?

Annnddddd... you directly copy & pasted it in.

Gotcha.

Guest Feb 10, 2019
edited by Guest  Feb 10, 2019
edited by Guest  Feb 10, 2019