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The "roots" of a polynomial are the solutions of the equation polynomial = 0. That is, any value which you can replace for "x", to make the polynomial equal to zero.
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Roots of a polynomial that can be written in the form p q are called roots?
Rational roots
The polynomial given roots?
Do mean find the polynomial given its roots ? If so the answer is (x -r1)(x-r2)...(x-rn) where r1,r2,.. rn is the given list roots.
What is the polynomial roots to 1 5i and -3i?
4
How to tell if there are no real roots?
The real roots of what, exactly? If you mean a square trinomial, then: If the discriminant is positive, the polynomial has two real roots. If the discriminant is zero, the polynomial has one (double) real root. If the discriminant is negative, the polynomial has two complex roots (and of course no real roots). The discriminant is the term under the square root in the quadratic equation, in other words, b2 - 4ac.
Roots of a polynomial that can be written in the form p over q are called roots?
of the rational function p(x)/q(x). These roots are the values of x that make the numerator, p(x), equal to zero. In other words, they are the solutions to the equation p(x) = 0.
How many real roots will a 3rd degree polynomial have?
A third degree polynomial could have one or three real roots.
Why is roots of even or odd hurwitz polynomial found on the jw axis only?
Actually, the roots of a Hurwitz polynomial are in the left half of the complex plain, not on the imaginary axis. As for the reason, that is because the polynomial is DEFINED to be one that has that kind of roots.
What is the relationship between the degree of a polynomial and the number of roots it has?
In answering this question it is important that the roots are counted along with their multiplicity. Thus a double root is counted as two roots, and so on. The degree of a polynomial is exactly the same as the number of roots that it has in the complex field. If the polynomial has real coefficients, then a polynomial with an odd degree has an odd number of roots up to the degree, while a polynomial of even degree has an even number of roots up to the degree. The difference between the degree and the number of roots is the number of complex roots which come as complex conjugate pairs.
Roots of a polynomial that can be written in the form p q are called roots?
Rational roots
The polynomial given roots?
Do mean find the polynomial given its roots ? If so the answer is (x -r1)(x-r2)...(x-rn) where r1,r2,.. rn is the given list roots.
At most how many unique roots will a fourth degree polynomial have?
4, the same as the degree of the polynomial.
At most how many unique roots will a third-degree polynomial have?
A third-degree equation has, at most, three roots. A fourth-degree polynomial has, at most, four roots. APEX 2021
What is the polynomial roots to 1 5i and -3i?
4
How to tell if there are no real roots?
The real roots of what, exactly? If you mean a square trinomial, then: If the discriminant is positive, the polynomial has two real roots. If the discriminant is zero, the polynomial has one (double) real root. If the discriminant is negative, the polynomial has two complex roots (and of course no real roots). The discriminant is the term under the square root in the quadratic equation, in other words, b2 - 4ac.
Is it true that the degree of polynomial function determine the number of real roots?
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.)
What is the minimum number of roots an odd powered polynomial will have?
1
how many roots does the graphed polynomial function have?
here is the graph
