Question

Find a polynomial function with leading coefficient 1 that has the given zeros, multiplicities, and degree. zero: 1, multiplicity: 2 zero: 2, multiplicity: 2 degree: 4

Answer 1

Polynomial expression for the given  conditions is formulated in the equation

y(x)=1*(x-2)^3(x-0)^2

The polynomial for the conditions with leading coefficient 1 that has the given zeros, multiplicities, and degree. Zero: 2, multiplicity: 3 Zero: 0, multiplicity: 2 Degree: 5 is given as

According to the given condition

The given conditions to write the polynomial equations are as follows

Zero 2  and Multiplicity 3

Zero 0 and Multiplicity 2  

Degree of polynomial expression  = 5

The leading coefficient of polynomial expression = 1

Let us consider the polynomial equation has only one variable and hence in the general form we can write the equation of polynomial as follows

From the general form of polynomial expression as shown in equation (1) we can write

Polynomial expression for the given  conditions is formulated in the equation

y(x)=1*(x-2)^3(x)^2-------(2)

So the polynomial for the conditions given in the question is expressed as

y(x)=1*(x-2)^3(x)^2

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