DarkBlueChocobo
  • DarkBlueChocobo
Help with quadratic inequalities
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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DarkBlueChocobo
  • DarkBlueChocobo
\[x^2 -6>-5x\]
mathstudent55
  • mathstudent55
Move the -5x to the left, and factor the left side. What do you get?
DarkBlueChocobo
  • DarkBlueChocobo
so we have to get it to one side If I understand so \[x^2 + 5x -6 > 0\]

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mathstudent55
  • mathstudent55
Good
DarkBlueChocobo
  • DarkBlueChocobo
(x+6)(x-1) I believe would be the factors
mathstudent55
  • mathstudent55
Good. Now pretend it's an equation, and find the zeros. (x + 6)(x - 1) = 0
DarkBlueChocobo
  • DarkBlueChocobo
x= -6 x= 1
mathstudent55
  • mathstudent55
Great. Now we move on to a number line. Since the inequality sign is strictly >, and not >=, mark open circles on the number line at the zeros of the equation.
DarkBlueChocobo
  • DarkBlueChocobo
|dw:1438830581670:dw|
mathstudent55
  • mathstudent55
Great. Now we write the factored inequality below the number line, so we can use it easily. |dw:1438830704607:dw|
mathstudent55
  • mathstudent55
The two zeros of the equation are two points of interest for us. They divide the number line into 3 regions (not counting the points of interest). Now we pick a number from each region and test in the factored inequality. If the number works, we darken the entire region the number is in.
mathstudent55
  • mathstudent55
|dw:1438830839108:dw|
DarkBlueChocobo
  • DarkBlueChocobo
so 3 regions would be negative positive and 0? or
mathstudent55
  • mathstudent55
Notice that since we are comparing with zero, if -7 in the two factors is negative, we know negative times negative is positive, so it works. The left region works. |dw:1438830935258:dw|
DarkBlueChocobo
  • DarkBlueChocobo
so could we test 2?
mathstudent55
  • mathstudent55
Yes, you can test 2. Now we test a number from the middle region. Zero is always easy to check.
DarkBlueChocobo
  • DarkBlueChocobo
|dw:1438831031694:dw|
DarkBlueChocobo
  • DarkBlueChocobo
|dw:1438831123797:dw|
mathstudent55
  • mathstudent55
I tested 2 above. It is from the right region, and it works, sotot he right of 1 it works. |dw:1438831029172:dw|
geerky42
  • geerky42
Or you can tell by which way parabola opens. For this problem, you have parabola opening upward, so you have left and right region.
mathstudent55
  • mathstudent55
Zero does not work, so the middle region does not work, so we do not color it in. |dw:1438831166432:dw|
DarkBlueChocobo
  • DarkBlueChocobo
So we have (-inf,-6) U (1,inf)?
geerky42
  • geerky42
Yeah.

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