Find the equation for the polynomial function with the following information: degree 3
zero at 1 with multiplicity 1, zero at 2 with multiplicity 1, and zero at -1 with multiplicity 3.
y-intercept at 2

y = x⁵ - 4x³ - 2x² + 3x + 2

Step-by-step explanation:

There is a major disconnect in your question.

The sum of your multiplicities must equal the degree of the polynomial.

IF

we ASSUME that the multiplicity sum is correct and the polynomial degree is not 3 but 5

THEN

y = (x - 1)(x - 2)(x + 1)(x + 1)(x + 1)

y = (x - 1)(x - 2)(x + 1)(x² + 2x + 1)

y = (x - 1)(x - 2)(x³ + 3x² + 3x + 1)

y = (x - 1)(x⁴ + x³ - 3x² - 5x - 2)

y = x⁵ - 4x³ - 2x² + 3x + 2

A quick plot shows that our zeros and y intercept are correct and the curve shapes at the zeros display the correct characteristics for the multiplicities.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions