Mathematics: Find all the real and complex zeros of f(x)=x^3-7x^2+4x-28

Find all the real and complex zeros of f(x)=x^3-7x^2+4x-28

mikiahpowell92

16.03.2022

For $x \in\mathbb{C}$

x = -2i

x = 2i

x = 7

Step-by-step explanation:

f(x)=x^3-7x^2+4x-28

For f(x) = 0

x^3-7x^2+4x-28 = 0

We can easily factor the expression x^3-7x^2+4x-28 by grouping.

$x^3-7x^2+4x-28 = (x^3-7x^2)+(4x-28) = x^2(x-7)+4(x-7) = \boxed{(x^2+4)(x-7) }$

Now we have

(x^2+4)(x-7) = 0

Therefore,

$x^2+4 = 0 \text{ or } x-7 = 0$

So,

$x^2 = -4 \implies x = \pm\sqrt{-4}$

Once $\sqrt{-1} = i$

$x = \pm\sqrt{-4} = \pm\sqrt{4}\sqrt{-1} = \pm 2i$

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asiaboo37

07.05.2021

1 = 50

2 = 90

3 = 60

4 = 60

5 = 60

6 = 60

7 = 100

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