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

the volume is the product of the area of the base, 3x(3x+4), and the height, 3x-1

step-by-step explanation:

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.