Mathematics, 04.11.2019 19:31 iesps010411

According to the fundamental theorem of algebra how many roots exits for the polynomial function. f(x)=8x^7-x^5+x^3+6

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The Fundamental Theorem of Algebra (FTOA) tells us that any non-zero polynomial in one variable with complex (possibly real) coefficients has a complex zero.

A straightforward corollary, often stated as part of the FTOA is that a polynomial in a single variable of degree

with complex (possibly real) coefficients has exactly

complex (possibly real) zeros, counting multiplicity.

To see that the corollary follows, note that if

(

)

is a polynomial of degree

and

(

)

, then

(

−

)

is a factor of

(

)

and

(

)

−

is a polynomial of degree

−

. So repeatedly applying the FTOA, we find that

(

)

has exactly

complex zeros counting multiplicity.

Discriminants

If you want to know how many real roots a polynomial with real coefficients has, then you might like to look at the discriminant - especially if the polynomial is a quadratic or cubic. Ths discriminant gives less information for polynomials of higher degree.

The discriminant of a quadratic

is given by the formula:

−

Then:

indicates that the quadratic has two distinct real zeros.

indicates that the quadratic has one real zero of multiplicity two (i.e. a repeated zero).

indicates that the quadratic has no real zeros. It has a complex conjugate pair of non-real zeros.

The discriminant of a cubic

is given by the formula:

−

Then:

indicates that the cubic has three distinct real zeros.

indicates that the cubic has either one real zero of multiplicity

or one real zero of multiplicity

and another real zero.

indicates that the cubic has one real zero and a complex conjugate pair of non-real zeros.

Step-by-step explanation:

Answer from: Quest

One unique triangle, because those angles add up to 180, and that's how many degrees there are in one triangle.

Answer from: Quest

you would need to know all the numbers that are on there

step-by-step explanation:

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