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Write the expression in quadratic form, if possible. x^(4) + 12x^(2) - 8

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Final answer:

The expression
x^(4) + 12x^(2)- 8 can be put into quadratic form by substituting t =
x^(2) resulting in
t^(2)+ 12t - 8 = 0. This new equation is in standard quadratic form a
t^(2)+ bt + c= 0, and can be solved using the quadratic formula.

Step-by-step explanation:

To write the expression
x^(4)+ 12x^(2) - 8 in quadratic form, we can let t =
x^(2). This substitution gives us a quadratic expression in terms of t:
t^(2) + 12t - 8. Now we have a quadratic equation of the form
at^(2)+ bt + c = 0, where a = 1, b = 12, and c = -8.

We can solve this quadratic equation using the quadratic formula, which states that for any quadratic equation of the form
at^(2) + bt + c = 0, the solutions for t are given by:

t = (-b ± √(
b^(2) - 4ac)) / (2a)

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