Question

Find the complex zeros of the following polynomial tunction and use the complex zeros to factor f

Answer 1

Answer:

x = 5 or x = 5 + 2 i or x = 5 - 2 i

Step-by-step explanation:

Solve for x:

x^3 - 15 x^2 + 79 x - 145 = 0

Hint: | Factor the left-hand side.

The left hand side factors into a product with two terms:

(x - 5) (x^2 - 10 x + 29) = 0

Hint: | Find the roots of each term in the product separately.

Split into two equations:

x - 5 = 0 or x^2 - 10 x + 29 = 0

Hint: | Look at the first equation: Solve for x.

Add 5 to both sides:

x = 5 or x^2 - 10 x + 29 = 0

Hint: | Look at the second equation: Solve the quadratic equation by completing the square.

Subtract 29 from both sides:

x = 5 or x^2 - 10 x = -29

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 25 to both sides:

x = 5 or x^2 - 10 x + 25 = -4

Hint: | Factor the left-hand side.

Write the left hand side as a square:

x = 5 or (x - 5)^2 = -4

Hint: | Eliminate the exponent on the left-hand side.

Take the square root of both sides:

x = 5 or x - 5 = 2 i or x - 5 = -2 i

Hint: | Look at the second equation: Solve for x.

Add 5 to both sides:

x = 5 or x = 5 + 2 i or x - 5 = -2 i

Hint: | Look at the third equation: Solve for x.

Add 5 to both sides:

Answer: x = 5 or x = 5 + 2 i or x = 5 - 2 i