Question

Find all the zeroes of the polynomial function f(x)=x^3-5x^2+6x-30 in you use synthetic division show all three lines of numbers

Answer 1

Answer:

5,$i\sqrt 6$ and $-i\sqrt 6$

Step-by-step explanation:

We are given that  the polynomial

$f(x)=x^3-5x^2+6x-30$

We have to find the all the zeroes of the polynomial function.

$f(x)=0$

$x^3-5x^2+6x-30=0$

$x^2(x-5)+6(x-5)=0$

$(x-5)(x^2+6)=0$

$x-5=0$

$x=5$

$x^2+6=0$

$x^2=-6$

$x=\pm\sqrt{-6}=\pm i\sqrt6$

Using $\sqrt{-1}=i$

Hence, all the zeroes of the polynomial function are

5,$i\sqrt 6$ and $-i\sqrt 6$