# Can a degree 4 polynomial with real coefficients have exactly 0 real roots?

## Can a degree 4 polynomial with real coefficients have exactly 0 real 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.

Can a 4th degree function have exactly 3 real zeros?

A fourth degree polynomial has four roots. Non-real roots come in conjugate pairs, so if three roots are real, all four roots are real. If there are only three distinct real roots, one root is duplicated. Therefore, your polynomial factors as p(x)=(x−a)2(x−b)(x−c).

How many zeros can a degree 4 polynomial have?

one zero
This function is zero for only one value of x , namely x=0 . So in one sense you could say that it has one zero. By the Fundamental Theorem of Algebra, any quartic equation in one variable has exactly 4 roots – counting multiplicity. In this particular example, it has one root of multiplicity 4 , namely x=0 .

### How many real zeros can a 4th degree polynomial have?

How many zeros does a 4th degree polynomial have? – Quora. It has up to four zeroes. The minimum amount of zeroes is zero if you don’t count complex zeroes and one if you do. Fourth-degree polynomials are also known as quartic polynomials.

How do you know if a polynomial has real roots?

The terms solutions/zeros/roots are synonymous because they all represent where the graph of a polynomial intersects the x-axis. The roots that are found when the graph meets with the x-axis are called real roots; you can see them and deal with them as real numbers in the real world.

How do you know how many zeros a polynomial has?

Explanation: In order to determine the positive number of real zeroes, we must count the number of sign changes in the coefficients of the terms of the polynomial. The number of real zeroes can then be any positive difference of that number and a positive multiple of two.

#### Does every quartic function have 4 zeros?

This function is zero for only one value of x , namely x=0 . By the Fundamental Theorem of Algebra, any quartic equation in one variable has exactly 4 roots – counting multiplicity.

How to find the zeros of a fourth degree polynomial?

Finding The Zeros of Fourth Degree Polynomial. A polynomial is an expression of the form ax^n + bx^ (n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values of x for which the value of the polynomial is zero. To find the zeros of a polynomial by grouping,…

Are there real zeros in a polynomial function?

A polynomial function of degree n, has at most n real zeros. Proof The proof is based on the Factor Theorem. If r is a zero of a polynomial function then and, hence, is a factor of Each zero corre- sponds to a factor of degree 1.Because cannot have more first-degree factors than its degree, the result follows.

## Can a polynomial of degree k be a zero?

This tells us that k is a zero. This pair of implications is the Factor Theorem. As we will soon see, a polynomial of degree n in the complex number system will have n zeros. We can use the Factor Theorem to completely factor a polynomial into the product of n factors.

Is the remainder of a polynomial a factor?

The remainder is zero, so (x + 2) is a factor of the polynomial. We can use the Division Algorithm to write the polynomial as the product of the divisor and the quotient: By the Factor Theorem, the zeros of x3 − 6×2 − x + 30 are –2, 3, and 5.