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3 years ago

Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros 2+i, 2

1 answer:

8 0

x^3 - 6x^2 + 13x - 10 We have been given the roots 2+i and 2, so two of the factors in the desired polynomial is (x - 2) = 0 (x - 2 -i ) = 0 Let's create a third root by negating the sign of the imaginary component to create the complex conjugate of the known complex root. (x - 2 + i) = 0 Now multiple (x - 2 - i) and (x - 2 + i) (x - 2 - i) (x - 2 + i) x^2 - 2x - xi -2x +4 +2i xi -2i - (-1) x^2 -4x +4 + 1 x^2 -4x + 5 And we've cancelled the imaginary term. Let's multiply this quadratic equation by the remaining factor. x^2 -4x + 5 x - 2 x^3 - 4x^2 + 5x -2x^2 +8x -10 = x^3 -6x^2 + 13x - 10 So the desired polynomial is x^3 - 6x^2 + 13x - 10

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The area of a rectangle is 64 square centimeters. The rectangle is 4 centimeters wide. How long is the rectangle.

VLD [36.1K]

The Area is the width times the height: A = w x h;
Then, 64 = w x h;
h = 4 + w;
64 = 4w + w^2;
w^2 + 4w - 64 = 0;
We solve this equation: w1 ≈ 6,24 > 0 (okay); w2 ≈ - 10,24 < 0 (not okay);
Finally, h1 ≈ 10,24;

4 0

3 years ago

The speed of the current in a creek is 5 mph. A person clan kayak 3 mi upstream in the same time that it takes him to kayak 13 m

Brut [27]

Answer:

Step-by-step explanation:

0) the basic formula is: L=v*t, where L - distance, v - speed/velocity; t - time;

1) if the person's speed in still water is 'v' and the speed of water is 5 (according to the condition), then the upstream speed is 'v-5' and the downstream speed is 'v+5';

2) according to the condition the upstream time and the downstream time are the same, it means t₁=t₂=t, where t₁=upstream time and t₂=downstream time;

3) according to the items above it is possible to make up the equation of the upstream travel: t(v-5)=3; ⇒ t=3/(v-5);

4) according to the items above it is possible to make up the equation of the downstream travel: t(v+5)=13; ⇒ t=13/(v+5);

5) if t=3/(v-5) and t=13/(v+5), then

$\frac{3}{v-5} =\frac{13}{v+5}; \ => \ v=8.$

8 0

3 years ago

Which equation has the solution x = 3?

dybincka [34]

Answer:

2x + 4 = 10 = x =3

Step-by-step explanation:

09 - 31 = 0 (the variable x is not present in the given system)

0 +5=6 (the variable x is not present in the given system)

2x + 4 = 10 = x = 3

09-1=4 (the variable x is not present in the given system)

51 - 7 = 1 (the variable x is not present in the given system)

3x + 1 = 9 = x = 8/3

6 0

3 years ago

Explain and I will give the best answer brainiest.

dlinn [17]

Answer:

Well the Regular would be 3,2 and the reflection would be 3,-2

Step-by-step explanation:

the regular is already plotted x comes before y that is why the order is like that the square the regular is in is +,+ the reflection is +,- showing why the order is like that hope this helps!

4 0

3 years ago

Please answer asap!!!

Luba_88 [7]

Answer:

The triangles are realated because there the same size so the triangles are equal

Step-by-step explanation:soory if i did not help

4 0

3 years ago