Efficient Methods for Solving Quadratic Inequalities

[davon806]

Homework Statement

Hi,
there are several methods to solve an quadratic inequality.
1:by graph
2:if (x-a)(x-b) > 0,(x-a) > 0 and (x-b) > 0 or (x-a) < 0 and (x-b) < 0...
3.Using test value method
i.e.Find a and b in the expanded form of (x-a)(x-b)
a and b are the critical values,then we take a value of x from different interval and check whether it satisfies the
inequality or not.

Homework Equations

The Attempt at a Solution

We need to factorize before using method 2 and 3.
Is there any method to solve an quadratic inequality without factorizing?

 

[SammyS]

Homework Statement

Hi,
there are several methods to solve an quadratic inequality.
1:by graph
2:if (x-a)(x-b) > 0,(x-a) > 0 and (x-b) > 0 or (x-a) < 0 and (x-b) < 0...
3.Using test value method
i.e.Find a and b in the expanded form of (x-a)(x-b)
a and b are the critical values,then we take a value of x from different interval and check whether it satisfies the
inequality or not.

Homework Equations

The Attempt at a Solution

We need to factorize before using method 2 and 3.
Is there any method to solve an quadratic inequality without factorizing?

By factoring the quadratic into (x-a)(x-b) you are essentially solving a quadratic equation.

Rather than doing the factoring, use the quadratic formula to find the two roots, a and b. The answer will be the same as if you factored the quadratic, provided that certain basic conditions are met.

 

[davon806]

thx!