Find the number of roots for each equation.5. 5x4 + 12x3 – x2 + 3x + 5 = 0

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 .