The degree of a quadratic equation is always 2
The substitution that rewrites [tex]x^8 - 3x^4 +2 = 0[/tex] as a quadratic equation is [tex]u = x^4[/tex]
The equation is given as:
[tex]x^8 - 3x^4 +2 = 0[/tex]
Express 8 as 4 * 2
[tex]x^{4 \times 2} - 3x^4 +2 = 0[/tex]
Rewrite the equation as:
[tex](x^{4})^2 - 3x^4 +2 = 0[/tex]
Represent x^4 with u.
So, the equation becomes
[tex]u^2 - 3u +2 = 0[/tex]
Notice that the above equation has a degree of 2.
Hence, the substitution is [tex]u = x^4[/tex]
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