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goldenfox [79]
3 years ago
8

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

Mathematics
1 answer:
pav-90 [236]3 years ago
7 0

Answer:

The number of roots for  equation 5x^4 + 12x^3 – x^2 + 3x + 5 = 0 is 4 .

Step-by-step explanation:

Here, the given function polynomial is :

P(x) : 5x^4 + 12x^3 – x^2 + 3x + 5 = 0

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 5x^4 + 12x^3 – x^2 + 3x + 5 = 0 is 4 .

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