SOLUTION: Solve the inequality and express the solution in interval notation: x^2 - 6x + 11 <18

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Question 39031: Solve the inequality and express the solution in interval notation:
x^2 - 6x + 11 <18
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Solve the inequality and express the solution in interval notation:
x^2 - 6x + 11 <18
Look at the EQUALITY:
x^2 - 6x + 11 =18
x^2-6x-7=0
(x-7)(x+1)=0
x=7 or x=-1
So look at the interval (-1,7)
Zero is in this interval.
Look at 0^2-6(0)+11<18
This is true.
So the interval of all real numbers
between -1 and 7 is the solution-interval
for the inequality.
This is what it looks like:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=64 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 7, -1. Here's your graph:

Cheers,
Stan H.
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