Recall the Fundamental Theorem of Algebra, which says that if P(x) is a polynomial of degree n≥ 1, then P(x)=0 has exactly n roots.
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Practice makes perfect
We want to find the number of roots for the given equation.
Let's first rewrite it to have a polynomial written in standard form.
2-x^4+x^2=0 ⇔ - x^4+x^2+2=0
Recall the Fundamental Theorem of Algebra.
IfP(x)is a polynomial of degree n≥1,
thenP(x)=0has exactly nroots.
This rule includes rational roots, complex roots, and repeated roots. Since the degree of the polynomial on the left-hand side of the equation is 4, the equation has 4 roots.
