X^4 - 4x2 and 4x^2 - 9, solve the following?
2016-07-19 3:05 pm
This is unrelated, but I heard that the Quadratic Expression is involved when: a trinomial, with each expression being x^2 +2b + 2, if it was x^4, will the quadratic expression still be used?
回答 (2)
2016-07-19 3:10 pm
✔ 最佳答案
Yes, in some examples, when the appropriate change of variable is applied.x⁴ - 4x² = (x²)² - 4(x²) is a quadratic expression in x²
Let u = x²
x⁴ - 4x² = u² - 4u which is a quadratic expression in u
If the original 4th order polynomial has odd powers of x, then the quartic expression cannot be reduced to a quadratic in this manner, and extracting the roots of the polynomial is much more involved that simple application of quadratic techniques.
2016-07-19 3:09 pm
I think you mean factorization.
x⁴ - 4x²
= x² (x² - 4)
= x² (x² - 2²)
= x² (x + 2) (x - 2)
4x² - 9
= (2x)² - 3²
= (2x + 3) (2x - 3)
x⁴ - 4x²
= x² (x² - 4)
= x² (x² - 2²)
= x² (x + 2) (x - 2)
4x² - 9
= (2x)² - 3²
= (2x + 3) (2x - 3)
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