Use the given zero to find all the zeros of the function Use

Use the given zero to find all the zeros of the function.

Use the given zero to find all the zeros of the function. (Enter your answers as a comma-separated list. Include the given zero in your answer.) Function Zero f(x) = 4x3 + 5x2 + 36x + 45 3i x =______

Solution

f(x) = 4x³ + 5x² +36x +45

since complex zeros always comes in pair. So ( x+3i ) , (x-3i) are factors of f.

(x+3i) * ( x-3i) = x² - 9i²   ( i² = -1)

= x² +9

on dividing 4x³ + 5x² +36x +45 by x² +9 ie

4x³ + 5x² +36x +45 / x²+9 = 4x+5

so (4x+5) will be a factor of f.

(4x+5) = 0

x = -5/4

hence all zeros +3i, -3i , -5/4