Understanding Quadratic Inequality: Explained in Detail

[Lim Y K]

Can someone explain to be in detail what is quadratic inequality? It's rather confusing. Thank you

 

[jedishrfu]

There are some video tutorials on it that may help:

 

[tommyxu3]

Try to find the 2 roots of the quadratic equation and discuss the intervals made of these numbers.

 

[symbolipoint]

What is a quadratic inequality?
$$ax^2+bx+c<0$$or$$ax^2+bx+c<=0$$or$$ax^2+bx+c>0$$or$$ax^2+bx+c>=0$$

 

[symbolipoint]

To be clearer, do not let the relation to 0 fool you. The relation can be with a term or a value other than zero on one side. Merely adding the additive inverse to both sides can bring the inequality to relate a quadratic expression to zero. Also, if the quadratic is factorable, you may be able to have something like (ax+b)(cx+d) (relation-symbol)(0).

 

[Lim Y K]

For visualisation's sake, is it something like that? The space between the two intersection in the graph is equivalent to the space between he two lines on the number line?

 

[symbolipoint]

Lym Y K,
The Mathispower4u (which jedishru posted) video you should find very helpful in understanding what to do with solving a quadratic inequality. The roots of the quadratic expression form the x-number line into three intervals, and any value in each interval can be chosen to test the truth or falsity for the interval.

 

[symbolipoint]

The example in the paper in your included photograph shows $-4x^2-4x-1$ and we must assume it's meant as related versus 0. You can/should DIVIDE both sides by NEGATIVE 4, and this MUST reverse the direction of the inequality symbol. Why? because multiplication or division by a negative VALUE.
That step now gives you $x^2+x+1/4$ versus 0, as said, with relation reversed from what it was originally. This quadratic is factorable giving you exactly ONE critical x value.

$(x+1/2)^2$. versus 0. (You did not show on your paper the inequality symbol relating). The critical value is at $x=-1/2$, just one single value, cutting the x-number line into just two intervals. Now, you test each interval, and maybe also you need to test that critical x value of $-1/2$.