Question

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

Answer 1

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)