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almond37 [142]
3 years ago
10

Find the complex zeros of

E%7B2%7D%20%20%2B%2059x%20-%2087" id="TexFormula1" title=" f(x) = {x}^{3 } - 13 {x}^{2} + 59x - 87" alt=" f(x) = {x}^{3 } - 13 {x}^{2} + 59x - 87" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
timama [110]3 years ago
6 0

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

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Can someone help me with my homework I really don’t get it:(
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(I'll help you with the first one only because you need to learn this)

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Which table contains the vertex of the graph represented by y=x^2-6x+4?
Vaselesa [24]

vertex = (3,- 5 )

given a quadratic in standard form : y = ax² + bx + c ( a ≠ 0 ), then

the x-coordinate of the vertex is

x_{vertex} = - \frac{b}{2a}

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with a = 1, b = - 6 and c = 4, hence

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substitute this value into the equation for y- coordinate

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3 years ago
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4 0
3 years ago
When Tomas simplified the expression -2.6 + (-5.4), he got 2.8. what mistake did Tomas likely make?
vladimir2022 [97]

Tomas used incorrectly the rule of signs, the expression should be simplified as follows:

-2.6 + (-5.4)

-2.6 -5.4 = 8

<h3></h3><h3>What mistake did Tomas likely make?</h3>

Here Tomas wants to perform an addition between two numbers:

-2.6 + (-5.4)

And the outcome that Tomas gets is:

-2.6 + (-5.4) = 2.8

Here his mistake seems to bee that he thought the second number was a positive number, and he solved the operation:

-2.6 + 5.4

So, he used wrong the rule of signs.

Remember that the rule of signs says that:

(-)*(+) = (+)*(-) = (-)

Using that, we can rewrite the original expression:

-2.6 + (-5.4)

to:

-2.6 - 5.4

Solving that, we get:

-2.6 - 5.4 = -8

Which is the outcome that Tomas would have gotten if he had used correctly the rule of signs.

If you want to learn more about the rule of signs:

brainly.com/question/13333620

#SPJ1

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2 years ago
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