SOLUTION: I need help with the following question. My book does not have any examples or show any thing on this type of questions. [] is supposed to be a staight line up and down but I do

Algebra ->  Absolute-value -> SOLUTION: I need help with the following question. My book does not have any examples or show any thing on this type of questions. [] is supposed to be a staight line up and down but I do       Log On


   

Question 94447: I need help with the following question. My book does not have any examples or show any thing on this type of questions. [] is supposed to be a staight line up and down but I do not know how to due it.
Solve the absolute value equation or indication the equation has no solution. The answers are in solution sets with square roots in them
[2x^2-x-1]=3

Thank you
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the absolute value equation or indication the equation has no solution. The answers are in solution sets with square roots in them:
|2x^2 - x - 1| = 3; vertical lines are uppercase back-slash on my keyboard
:
We have two quadratic equation to solve
2x^2 - x - 1 = +3
2x^2 - x - 1 - 3 = 0
2x^2 - x - 4 = 0
and
2x^2 - x - 1 = -3
2x^2 - x - 1 + 3 = 0
2x^2 - x + 2 = 0
:
The first one can be solved using the quadratic formula:
a = 2; b = -1; c = -4
:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
:
x+=+%28-%28-1%29+%2B-+sqrt%28-1%5E2+-+4+%2A+2+%2A+-4+%29%29%2F%282%2A2%29+
:
x+=+%28%2B1+%2B-+sqrt%281+-+%28-32%29+%29%29%2F%284%29+
:
x+=+%28%2B1+%2B-+sqrt%281+%2B+32+%29%29%2F%284%29+
:
x+=+%28%2B1+%2B-+sqrt%2833%29%29%2F%284%29+
:
Two solutions:
x+=+%281+%2B+sqrt%2833%29%29%2F%284%29+
and
x+=+%281+-+sqrt%2833%29%29%2F%284%29+
:
:
The 2nd equation: 2x^2 - x + 2; has no real roots. We can see that by looking
at the discriminant: b^2 - 4*a*c. In this equation: a=2, b=-1, c=+2 so we have:
-1^2 - 4*2*2 = 1 - 16 = -15
Remember the discriminant rules. Less than 0, no real roots.
:
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