A leading coefficient of I, and zeros 3i and 2-i

f(x) = - 4x³ + 14x² - 36x + 45

Step-by-step explanation:

Given zeros x = a, x = b, then the factors are

(x - a) and (x - b)

and the polynomial is the product of the factors

Note that complex zeros occur in conjugate pairs

3i is a zero then - 3i is a zero

2 - i is a zero then 2 + i is a zero

The corresponding factors are

(x - 3i), (x - (- 3i), (x - (2 - i)) and (x - (2 + i)), that is

(x - 3i), (x + 3i), ((x - 2) + i), ((x - 2) - i)

Thus the polynomial is

f(x) = (x - 3i)(x + 3i)((x - 2) + i )((x - 2) - i) ← expand factors in pairs

     = (x² - 9i² )((x - 2)² - i² ) → i² = - 1

    = (x² + 9)(x² - 4x + 4 + 1)

   = (x² + 9)(x² - 4x + 5) ← distribute

   =   - 4x³ + 5x² + 9x² - 36x + 45 ← collect like terms

   = - 4x³ + 14x² - 36x + 45

all the angles opposite to the angle 150 would be 150 and all the angles that are next to 150 are 30 because they equal 180 it you add it up.

step-by-step explanation:

a rotation about point l

step-by-step explanation:

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