Can a polynomial of degree n have N 1 roots?

This can be proven easily by the fundamental Theorem of Algebra.

Is it true that every polynomial equation of degree n has n 1 real roots?

This is called the Fundamental Theorem of Algebra. If we insist on staying with real numbers, then the Fundamental Theorem says a bit less: every polynomial equation of degree n has at most n real roots. Thus the theorem holds for degree 1.

Does a polynomial of degree n always have n roots?

The Fundamental Theorem of Algebra says that a polynomial of degree n will have exactly n roots (counting multiplicity). This is not the same as saying it has at most n roots. To get from “at most” to “exactly” you need a way to show that a polynomial of degree n has at least one root.

How many zeros can a polynomial of degree n have N 1?

Answer Expert Verified A polynomial of n degree can have n zeros. For example, a quadratic equation ax² + bx + c = 0 can have 2 zeros, as the highest power of x is 2 or as the degree is 2.

How many roots does a polynomial of degree n have?

A polynomial of degree n can have only an even number fewer than n real roots. Thus, when we count multiplicity, a cubic polynomial can have only three roots or one root; a quadratic polynomial can have only two roots or zero roots.

What is the nth difference of a polynomial of degree n?

Answer:zero. Step-by-step explanation: ocabanga44 and 19 more users found this answer helpful. Thanks 15. 3.3.

Do all polynomials have n roots?

A polynomial of even degree can have any number from 0 to n distinct real roots. A polynomial of odd degree can have any number from 1 to n distinct real roots.

How many zeroes can a polynomial of degree n have * 1 point a almost N zeroes b atleast n zeroes C no zeroes D infinite zeroes?

How many zeroes can, a polynomial of degree n have? A polynomial of degree n has at the most n zeroes. ∴ 2, 1, 1 are the zeroes of x3 – 4×2 + 5x – 2. Hence verified.

When the degree of polynomial is 1 it is called?

A polynomial of degree 1 is know as linear polynomial. E.g.- Degree of polynomial 3x+5 is 1, thus it is a linear polynomial. Hence the required answer is linear polynomial.

What is a degree n polynomial?

A polynomial of degree n (in one variable, with real coefficients) is an expression of the form: The degree of a polynomial is the highest power of x whose coefficient is not 0. By convention, a polynomial is always written in decreasing powers of x.

Is it possible for a polynomial to have n+1 roots?

No, that is not possible. The only reason that a n degree polynomial has max n roots is because it can be written as a product of ‘n’ linear functions, as the product of n linear functions of x would yield a term having power x^n. You can not write a n degree polynomial into n+1 linear functions, no matter what you do.

How many $n$ turning points does a polynomial have?

A degree $n$ polynomial has at most $n$ roots (intersections with the $x$ axis). A “turning point” is a place where the derivative of the polynomial is zero (though not every place the derivative vanishes is a turning point), and since the derivative of a degree $n$ polynomial is a degree $n-1$ polynomial, there are at most $n-1$ turning points.

Can a polynomial have more than one solution?

Answer Wiki. A nth degree polynomial can have a maximum of n roots. If however it is satisfied by more than n values then it becomes an identity. An identity will not only have n solution, it will have infinite more solutions. So you can obviously find n+1 solutions. For example [math](x+1)^2=x^2+1+2x[/math] is a quadratic equation.