Solving Quadratic Inequality

[walsoncastro]

Also, parabola going up with x intercepts of (-3, 0) and (4, 0). Values in between -3 and 4, is below the x-axis

[CanalExtranho]

idk why but I like too much your way of speaking. Your voice is so good

[lucanijeanmarc]

Hi, i am french . Explainations are not the same in France ... It is complicaded . But this one is so easy for the pupils .. That is why i am going to teach this lesson to my daughter ..Thank you professor

[hardryv]

Fascinating, never saw that one before

[emalali]

I remember learning this in school and haven't forgotten. This seems so natural now.

[colinjava]

Another way (that I wouldn't do) which is purely algebraic, is:
x^2 - x - 12 < 0
(x+3)(x-4) < 0
So "x+3 < 0 and x-4 > 0" or "x+3 > 0 and x-4 < 0"
So "x < -3 and x > 4" or "x > -3 and x < 4"
so "No solution" or "-3 < x < 4"
so -3 < x < 4

[oryxisatthefront]

My professor taught me to just look at the inequality simbol and the sign of x^2: if the x^2 is positive and we have a > symbol or x^2 is negative and we have a < then the domain is of the values that are less than the smaller solution (in this case -3) and greater than the bigger solution (in this case 4). If x^2 is positive and we have a < symbol or x^2 is negative and we got a > symbol then the domain is every number between the two solutions. It seems like a lot through text but in practice it’s so much quicker (literally takes 2 seconds to find the domain) and way easier than having to plug the possible answers, especially as they get bigger (as another guy pointed out, it only works with quadratics)

[boody_tube]

Man u simplified the whole preparatory stage

[rmtfblz]

좋은 방법인 것 같습니다.

직관적인 그림으로 그려본다면

x-y 좌표평면에서

부등식의 좌측식을 x의 함수로 표현하면 : y = (x+3)(x-4)

위 2차함수를 그려보면 y<0인 영역은
-3<x<4 임을 알 수 있습니다.

[venkybabu]

Neg 3 and 4 means that the curves are dual. Like sine.

[moeberry]

Nice, now try solving a quadratic inequality that has only complex roots.

[xnstwdf]

I like to instead of using a number line to quickly sketch the graph with just the shape to see if I need to make the inequality between the critical values it outside of them

[Quicklearners]

You are a great teacher sir💯💯💯....i will make my students learn your tricks in my native language♥️Keep up the good work

[seventhunder]

That is good. Inequality was my weakness in school.

[aarututor]

wavy curve method is an easy method from exam point of view.
But understanding concepts is very important

[ronweisenstern]

If you find the roots you can just graph it and see where it is over 0 and where it is under 0

[RonnyS.]

Inequalities with intervals, thaks for helping me revise this, please also do Modulas Inequalities and Max Min With modulas.

[ayoubkhlifi]

mmmm from morocco, there is an easy way to do it, i don't know if you learned such a similar thing, we will consider as if we solve x^2-x-12=0
Delta=1-4*-12+=49
so there is two solutions:


we have ax^2 and a=1 which is positive.
so x^2-x-12 will be negative in :
]3;4[ , between this two numbers but 3 and 4 arent sulutions

[chebilya]

Good job but it's important to explain cases where the discriminant is less or equal to zero !

[dangerous_woman]

What about drawing + | - | + (with the rightmost + being the sign of the main coefficent)? If it's a rational function with division or multiplication you just multiply the signs of the terms with the biggest degree like [(+)(-)]/(+)=(-)