Writing Polynomial Functions from Complex Roots Answers

Write an equation for the cubic polynomial function shown. To find the equation of the function, first find the rangedomain✔ zeroes of the graph.

To solve for the leading coefficient, use a = –5(0 – 2)(0 – 3)(0 – 5) a = 5(0 – 2)(0 – 3)(0 – 5) 5 = a(0 – 2)(0 – 3)(0 – 5)✔ –5 = a(0 – 2)(0 – 3)(0 – 5).

The equation of the polynomial function is:

f(x) = x4 − [___]x3 + [___]x2 + [___]x − [___]

f(x) = x4 − [___]x3 + [___]x2 + [___]x − [___]

Write an equation for the cubic polynomial function whose graph has zeroes at 2, 3, and 5. Write the polynomial function for the graph.f(x) = (x – 2)(x – 3)(x – 5)Simplify the right side. What is the equation?

Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, –5).Write the equation of this cubic polynomial function. Recall that the zeroes are (2, 0), (3, 0), and (5, 0). What is the y-intercept of this graph?

Now, suppose one of the roots of the polynomial function is irrational. The roots of the function are 2, , and 5. Write the equation for this polynomial function. Which of the following must also be a root of the function?

Now, suppose one of the roots of the polynomial function is complex. The roots of the function are 2 + i, and 5. Write the equation for this polynomial function. Which of the following must also be a root of the function?

The linear factors of the cubic are ✔ (x – 2)(x – 3)(x – 5)(x – 2)(x – 3)(x – 5)(x + 5)(x + 2)(x + 3)(x + 5)(x + 2)(x + 3)(x – 5).

The equation of the polynomial function is:

The equation of the polynomial function is:

f(x) = x4 − [___]x3 + [___]x2 + [___]x − [___]

f(x) = x3 − [___]x2 + [___]x − [___]

f(x) = x4 − [___]x3 + [___]x2 + [___]x − [___]

f(x) = x3 − [___]x2 + [___]x − [___]

f(x) = x3 − [___]x2 + [___]x − [___]

Write an equation for the cubic polynomial function whose graph has zeroes at 2, 3, and 5. [image 1] Can any of the roots have multiplicity? [image 2] How can you find a function that has these roots?