1
vote
3answers
157 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 : $x^2 − 6 |x − 2| − 28 = 0$ $x^2 − 6 |x − 2| − 28 = 0$ ...
0
votes
1answer
96 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 $x<a, |x-a|=-(x-a)$ ...
2
votes
3answers
4k views

Taking the square roots in inequalities

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 ...
1
vote
4answers
300 views

Is it possible to take the absolute value of both sides of an equation?

I have a problem that says: Suppose $3x^2+bx+7 > 0$ for every number $x$, Show that $|b|<2\sqrt21$. Since the quadratic is greater than 0, I assume that there are no real solutions since $y = ...
1
vote
3answers
714 views

Quadratic equation with absolute value

Prepping for the GMAT, I came across the following question: What is the product of all solutions of: $$x^2 - 4x + 6 = 3 - |x - 1|?$$ First, I set up two equations, ie: $$x^2 - 4x + 6 ...