SOLUTION: I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Solving Polynomial Equ

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Question 166928This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been struggling to figure out this math problem and I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!
Solving Polynomial Equations.
Solve. Identify all multiple roots.
(x^2-3)^2+(x^2-3)-2=0 This question is from textbook Algebra and Trigonometry Structure and Method book 2

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Identify all multiple roots.
(x^2-3)^2+(x^2-3)-2=0
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Substitution: Let w = x^2-3
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You get: w^2 + w -2 = 0
Factor to get:
(w+2)(w-1) = 0
w = -2 or w = 1
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Solve for "x":
If w = -2, then
x^2-3 = -2
x^2 = 1
x = 1 or -1
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If w = 1, then
x^2-3 = 1
x^2 = 4
x = 2 or x = -2
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Cheers,
Stan H.