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puteri [66]
3 years ago
8

Check all of the correct solutions to this problem

Mathematics
1 answer:
MA_775_DIABLO [31]3 years ago
8 0

To solve a quadratic equation ax^2+bx+c=0 we can use the quadratic formula:

x_{1,2} = \cfrac{-b\pm\sqrt{b^2-4ac}}{2a}

In your case, the equation is identified by a=c=1,\ b=-5

So, the solving formula yields

x_{1,2} = \cfrac{5\pm\sqrt{25-4}}{2} = \cfrac{5\pm\sqrt{21}}{2}

So, the two solutions are derived by choosing the plus sign once, and the minus sign the other time:

x_{1} = \cfrac{5+\sqrt{21}}{2},\quad x_{2} = \cfrac{5-\sqrt{21}}{2}

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Un móvil azul de 573 g se encuentra en movimiento sobre un carril metálico. Si sobre el móvil, el resorte ejerce una fuerza haci
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Answer:

The total mechanical energy is 0.712 J.

Step-by-step explanation:

A blue 573 g mobile is moving on a metal rail. If on the mobile, the spring exerts a force to the right of modulus 0.85 N and in the indicated position the kinetic energy of the mobile-spring system is 0.47 J and its elastic potential energy is 0.242 J. Determine the mechanical energy of the system mobile-spring in the position shown as indicated in the figure.

The total mechanical energy is given by the sum of the kinetic energy and the potential energy.

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Potential energy = 0.242 J

The total mechanical energy is

T = 0.47 + 0.242 = 0.712 J

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Step-by-step explanation:

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Step-by-step explanation:

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Find all roots given that x = 3 + i is a solution. <br><br> x^4 - 10x^3 + 29x^2 - 10x - 50 = 0
Basile [38]

Answer:

x = 3 + i, x = 3 - i , x = 5 , and x = -1

Step-by-step explanation:

We know that given the polynomial with real coefficients, if x = 3 + i is a root, then x = 3 - i must be another root. These two roots can combine multiplicative factors as shown:

(x - 3 - i) * (x - 3 + i) = (x-3)^2 + 1 = x^2 - 6 x + 9 + 1 = x^2 - 6 x + 10

Then we divide the given polynomial: x^4 - 10x^3 + 29x^2 - 10x - 50  by the quadratic one we just found, and get a perfect division:

{x^4 - 10x^3 + 29x^2 - 10x - 50} / {x^2 - 6 x + 10} = x^2 - 4 x - 5

which can be factored out by grouping as shown below:

x^2 - 4 x - 5 = x^2 - 5 x + x - 5 = x (x - 5) + x - 5 = (x - 5 ) * (x + 1)

then the full factor form of the quartic polynomial given is:

(x - 3 - i) * (x - 3 + i) * (x - 5 ) * (x + 1)

and therefore the associated roots are:

x = 3 + i, x = 3 - i , x = 5 , and x = -1

5 0
3 years ago
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