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Q: At most how many unique roots will a fourth-degree polynomial have?

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It can have 1, 2 or 3 unique roots.

4, the same as the degree of the polynomial.

5, Using complex numbers you will always get 5 roots.

A third-degree equation has, at most, three roots. A fourth-degree polynomial has, at most, four roots. APEX 2021

A third degree polynomial could have one or three real roots.

Four.Four.Four.Four.

1

Sort of... but not entirely. Assuming the polynomial's coefficients are real, the polynomial either has as many real roots as its degree, or an even number less. Thus, a polynomial of degree 4 can have 4, 2, or 0 real roots; while a polynomial of degree 5 has either 5, 3, or 1 real roots. So, polynomial of odd degree (with real coefficients) will always have at least one real root. For a polynomial of even degree, this is not guaranteed. (In case you are interested about the reason for the rule stated above: this is related to the fact that any complex roots in such a polynomial occur in conjugate pairs; for example: if 5 + 2i is a root, then 5 - 2i is also a root.)

None, it involves the square root of a negative number so the roots are imaginary.

Upto 4. If the coefficients are all real, then it can have only 0, 2 or 4 real roots.

Such an equation has a total of six roots; the number of real roots must needs be even. Thus, depending on the specific equation, the number of real roots may be zero, two, four, or six.

Descartes' rule of signs (see related link) can help you determine the maximum number of real roots. If the polynomial is odd powered, then there will be at least one real root. Any even powered polynomial can be factored into a bunch of quadratics [though they may not be rational or even pretty], and any odd-powered polynomial can be factored into a bunch of quadratics and one linear (this one would have the real root). So the quadratics may have pairs of real or complex roots (having an imaginary component).To clarify, when I say complex, I'm referring to the fact that there will be an imaginary component to the root, because actually the real numbers is a subset of the set of complex numbers.The order of the polynomial will tell you how many roots it will have. If you can graph the polynomial, then you can see if it crosses the x axis. If it is a 5th order polynomial, and crosses the x axis 3 times, then there are 3 real roots (the other two roots are complex).

A polynomial can have as many 0s as its order - the power of the highest term.A polynomial can have as many 0s as its order - the power of the highest term.A polynomial can have as many 0s as its order - the power of the highest term.A polynomial can have as many 0s as its order - the power of the highest term.

Each distinct real root is an x-intercept. So the answer is 4.

No. A polynomial can have as many degrees as you like.

As many as you like. The highest power of the variable in question (usually x) defines the degree of the polynomial. If the degree is n, the polynomial can have n+1 terms. (If there are more then the polynomial can be reduced.) But there is NO LIMIT to the value of n.

A trinomial is a polynomial. All trinomials are polynomials but the opposite is not true. a trinomial= three unlike terms. a polynomial= "many" unlike terms.

The terms in a polynomial are seperated by a + or - So in given polynomial there are 4 terms.... abc , e, fg and h²

4

NONE If both roots are imaginary, the means the parabola does NOT cross the x-axis at all. The place where a function crosses the x- axis has the coordinate (x,0) for some value of x. That means if you plug in x to the function or polynomial, you get 0. This is equivalent to saying that x is a root of the polynomial. But if the only roots are imaginary, there will be no point (x,0) for any real number x.

As many as you like. A polynomial in 1 variable, and of degree n, can have n+1 terms where n is any positive integer.

I assume that should read:y = (x-8)(x+3)^2 (where the "^" stands for power) Since the polynomial is already factored, it is clear that it has the roots 8, -3, and -3; in other words, three roots (including one double root); or two, if you count the duplicates only once.

how many roots does dicotyledons ave

No. Complex zeros always come in conjugate pairs. So if a+bi is one zero, then a-bi is also a zero.The fundamental theorem of algebra says"Every polynomial equation of degree n with complex coefficients has n roots in the complex numbers."If you want to know how many complex root a given polynomial has, you might consider finding out how many real roots it has. This can be done with Descartes Rules of signsThe maximum number of positive real roots can be found by counting the number of sign changes in f(x). The actual number of positive real roots may be the maximum, or the maximum decreased by a multiple of two.The maximum number of negative real roots can be found by counting the number of sign changes in f(-x). The actual number of negative real roots may be the maximum, or the maximum decreased by a multiple of two.Complex roots always come in pairs. That's why the number of positive or number of negative roots must decrease by two. Using the two rules for positive and negative signs along with the fact that complex roots come in pairs, you can determine the number of complex roots.

2 roots

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