Answer:
The number of roots for equation [tex]5x^4 + 12x^3 – x^2 + 3x + 5 = 0[/tex] is 4 .
Step-by-step explanation:
Here, the given function polynomial is :
[tex]P(x) : 5x^4 + 12x^3 – x^2 + 3x + 5 = 0[/tex]
The Fundamental Theorem of Algebra says that a polynomial of degree n will have exactly n roots (counting multiplicity).
Now here, the degree if the polynomial is 4 (highest power of variable x).
So, according to the Fundamental Theorem, the given polynomial can have AT MOST 4 roots, counting Multiplicity.
Hence, the number of roots for equation [tex]5x^4 + 12x^3 – x^2 + 3x + 5 = 0[/tex] is 4 .
