# Tagged Questions

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### Absolute value quadratic inequalities not the usual?

$| -x^2 + 6x | \gt 13$,for example. I would start off solving $-x^2 + 6x = \pm 13$ and either get 4 solutions, 3 solutions or two simply do the the nature of the graph. Without knowing if the two ...
163 views

### Solve the equation : $x^2 − 6 |x − 2| − 28 = 0$

The following is an absolute value quadratic equation that I want to solve: $$x^2 − 6 |x − 2| − 28 = 0$$ Here is what I did : $x^2 − 6 |x − 2| − 28 = 0$ $x^2 − 6 |x − 2| − 28 = 0$ ...
104 views

### Determine all the values of the parameter $a$ for which the inequality $3-|x-a|>x^2$ is satisfied by at least one negative $x$.

I wanted to know, how can I determine all the values of the parameter $a$ for which the inequality $3 - |x-a| > x^2$ is satisfied by at least one negative $x$. I tried for $x<a, |x-a|=-(x-a)$ ...
I have a question regarding taking square roots in inequalities. I have a problem asking: Suppose $3x^2+bx+7>0$ for every real number x. Show that $|b|<2\sqrt{21}$. In an earlier question it ...