$f(x) = 0 \\\\\implies x^3-13x^2+59x -87 =0\\\\\implies x^3 -3x^2 -10x^2 +30x +29x - 87=0\\\\\implies x^2(x-3) - 10x(x-3) + 29(x-3) =0\\\\\implies (x-3)(x^2 -10x +29) =0\\\\\implies x - 3 = 0 ~~ \text{or}~~x^2 -10x +29 = 0\\\\\implies x =3~~ \text{ or} ~~ x = \dfrac{-(-10) \pm \sqrt{(-10)^2 -4 \cdot 1 \cdot 29}}{2(1)}\\\\\implies x =3~~ \text{ or} ~~ x = \dfrac{10\pm \sqrt{-16}}{2}\\\\\implies x =3~~ \text{ or} ~~ x = \dfrac{10\pm 4i }{2}\\$

$\\\implies x =3~~ \text{ or} ~~ x =5 \pm 2i\\\\\text{Hence the complex roots are,}~ 5- 2i ~~ \text{and} ~~5 + 2i$

6 0

2 years ago

For every 20 penguins at the North Pole there are 9 polar bears. If you encountered 27 polar bears, how many penguins would you

cluponka [151]

Answer:

60 penguins

Step-by-step explanation:

We need to find out how many times 9, the number of polar bears for every 20 penguins, was multiplied by, so that we can multiply 20 penguins by the same amount.

27/9 = 3

20*3 = 60

5 0

2 years ago

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