What are the zeroes of the function? what are their multiplicities?

= x4 – 4x3 + 3x2

Answer-

Zeros of the functions are 0 with multiplicity of 2 and 1, 3 with multiplicity of 1.

Solution-

The given polynomial is,

For calculating roots,

The root at x²=0, has multiplicity of 2 as the power is 2.

So, the graph will bounce at x=0

At x=1, x=3 the graph will go through the x axis. They have multiplicity of 1.

The zeroes of the function are . Multiplicity of is , multiplicity of is and the multiplicity of is .

Further explanation:

The given polynomial is .

The above polynomial is a biquadratic polynomial.

Consider the given polynomial as follows:

The polynomial is a polynomial of degree .

To find the zeroes of polynomial equate this polynomial to 0.

Factorize the polynomial by taking common term , since is the only lowest term in above polynomial with power .

Factorize the polynomial as follows:

Now, factorize the quadratic term as follows:

Substitute in the polynomial as shown below:

Now, from zero-product property the zeroes of the polynomial are shown below:

Here, is a zero of multiplicity , since the power of is .

Since, the degree of the polynomial is , therefore, there will be solution to this polynomial.

Thus, the zeroes of the function are with having multiplicity of and both and have multiplicity of .

Learn more:

1. Learn more about numbers link

2. Learn more about scientific notation of numbers link

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Polynomial

Keywords: Zeroes, function, multiplicity, x^4-4x^3+3x^2, degree, highest power, polynomial, quadratic, equation, zero-product property, factorization, biquadratic expression.

details

step-by-step explanation: