X^2

Question

Hi Bunuel,

What exactly is the solution for:

x^2 x(x-1)0 => x>1 ..OR.. x>0 , x-1 x 0x (signed changed)

I really appreciate your help.

-K

Bunuel · Answer

x^2 x(x-1) < 0 --> roots are 0 and 1 --> "<" sign indicates that the solution lies between the roots: 00 (x>1), which is not possible, x cannot be simultaneously less than zero and more than 1. x>0 and x-1<0 (x<1) --> 0x. x(x-1) > 0 --> roots are 0 and 1 --> ">" sign indicates that the solution lies to the left of a smaller root and to the right of the larger root: x<0 or x>1. Solving inequalities: x2-4x-94661.html#p731476 inequalities-trick-91482.html everything-is-less-than-zero-108884.html?hilit=extreme#p868863 xy-plane-71492.html?hilit=solving%20quadratic#p841486 Hope it helps.

kartik222 · Answer

thanks a lot bunuel!!

-K

KarishmaB · Answer

When solving such inequalities, keep in mind that it is not a good idea to cancel off variables. So x^2-x<0 => x(x-1)<0 and x^2>x => x(x-1) > 0 Now, check out this post for details on how to quickly solve x(x-1)<0 or x(x-1)>0 https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2012/06 ... e-factors/

vsprakash2003 · Answer

Thanks Karishma. Your article explained the concept clearly

EvaJager · Answer

For any quadratic inequation, here are steps that can be followed to solve it:

1) Write the inequation in the form  x^2+bx+c>0  or  x^2+bx+c0 , we look again at the graph of the parabola and find those values of  x  for which the graph is above the Y-axis.
We obtain the solution  x1.

Every upward parabola has its two "arms" above the X-axis for values of  x  outside the interval defined by the two roots, and it has the "arc" below the X-axis for values of  x  between the two roots.

This is the "justification" for how the sign of a quadratic expression changes in the three intervals defined by the two roots of the quadratic. Once you understand this, it will be really easy to quickly write down the solution for any similar inequation, and you will need just to imagine the parabola.

X^2<x absolute value question

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