Solving Quadratic Inequalities

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Quadratic means square. The equation which has the highest degree for the variable as two is called a quadratic equation. The general form of a quadratic equation is ax2 + b x + c = 0. Here x is the unknown variable and a. b. c are the constants. The sign of the variable ‘a’ decides if the shape of the quadratic equation is upward or downward. Inequalities are equations which contain the ‘>’ greater than or ‘<’ lesser than symbols.

Example 1: Solve the quadratic inequality x2 + 10x + 25 > 0.

Solution: Given here is the quadratic inequality x2 + 10 x + 25 > 0.

The first step is to solve for the quadratic inequality.

The equation can be written as x2 + 5x + 5x + 25 > 0

Now factoring the common terms gives x(x + 5) + 5(x + 5) > 0.

Hence (x + 5) (x + 5) > 0; x + 5 > 0.

Therefor x > -5 is the solution.
 
Example 2: Solve the quadratic inequality x2 - 9x + 18 < 0.

Solution: Given here is the quadratic inequality x2 – 9 x + 18 < 0.

The first step is to solve for the quadratic inequality.

The equation can be written as x2 - 3x - 6x + 18 < 0

Now factoring the common terms gives x(x - 3) – 6 (x - 3) < 0.

Hence (x - 3) (x - 6) < 0; this gives x -3 < 0 or x – 6 < 0.

Therefor x < 3 or x < 6 is the solution.

 

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