MATHEMATICS HIGH SCHOOL

How many roots do the following equations have? -12x^2 - 25x+5 +x^3=0

Answers

Answer 1

Answer:

Answer:

There are 3 roots of the given equation.

Step-by-step explanation:

Given the equation

$-12x^2-25x+5+x^3=0$

we have to tell the number of roots of the given equation.

As the number of roots for an equation is equal to degree.

The degree of a polynomial is the highest power of its monomials with non-zero coefficients.

Hence, number of roots is the highest power in the equation.

Now, the equation is $-12x^2-25x+5+x^3=0$

The highest power i.e degree of equation is 3.

hence, there are 3 roots of the given equation.

Answer 2

Answer: $-12x^2 - 25x + 5 + x^(3) = 0$
$x^(3) - 12x^(2) - 25x + 5 = 0$
$x = \sqrt[3]{((-b^(3))/(27a^(3)) + (bc)/(6a^(2)) - (d)/(2a)) + \sqrt{((-b^(3))/(27a^(3)) + (bc)/(6a^(2)) - (d)/(2a))^(2) + ((c)/(3a) - (b^(2))/(9a^(2)))^(3)}} + \sqrt[3]{((-b^(3))/(27a^(3)) + (bc)/(6a^(2)) - (d)/(2a)) - \sqrt{((-b^(3))/(27a^(3)) + (bc)/(6a^(2)) - (d)/(2a))^(2) + ((c)/(3a) - (b^(2))/(9a^(2)))^(3)}} - (b)/(3a)$
$x = \sqrt[3]{((-(-12)^(3))/(27(1)^(3)) + ((-12)(-25))/(6(1)^(2)) - (5)/(2(1))) + \sqrt{((-(-12)^(3))/(27(1)^(3)) + ((-12)(-25))/(6(1)^(2)) - (5)/(2(1)))^(2) + ((-25)/(3(1)) - (-(-25)^(2))/(9(1)^(2)))^(3)}} + \sqrt[3]{((-(-12)^(3))/(27(1)^(3))}} + ((-12)(-25))/(6(1)^(2)) - (5)/(2(1))) - \sqrt{((-(-12)^(3))/(27(1)^(3)) + ((-12)(-25))/(6(1)^(2)) - (5)/(2(1)))^(2) + ((-25)/(3(1)) - (-(-25)^(2))/(9(1)^(2)))^(3) - (-12)/(3(1))}}$
$x = \sqrt[3]{((-(-1728))/(27(1)) + (300)/(6(1)) - (5)/(2)) + \sqrt{((-(-1728))/(27(1)^(3)) + (300)/(6(1)) - (5)/(2))^(2) + ((-25)/(3(1)) - (144)/(9(1)))^(3)}}} + \sqrt[3]{((-(-1728))/(27(1)) + (300)/(6(1)) - (5)/(2)) - \sqrt{((-(-1728))/(27(1)^(3)) + (300)/(6(1)) - (5)/(2))^(2) + ((-25)/(3(1)) - (144)/(9(1)))^(3)}}} - (-12)/(3)$
$x = \sqrt[3]{((1728)/(27) + (300)/(6) - 2(1)/(2)) + \sqrt{((1728)/(27) + (300)/(6) - 2(1)/(2))^(2) + ((-25)/(3) - (144)/(9))^(3)}} + \sqrt[3]{((1728)/(27) + (300)/(6) - 2(1)/(2)) - \sqrt{((1728)/(27) + (300)/(6) - 2(1)/(2))^(2) + ((-25)/(3) - (144)/(9))^(3)}} - 4$
$x = \sqrt[3]{(64 + 50 - 2(1)/(2)) + \sqrt{(64 + 50 - 2(1)/(2))^(2) + (-8(1)/(3) - 16)^(3)}} + sqrt[3]{(64 + 50 - 2(1)/(2)) - \sqrt{(64 + 50 - 2(1)/(2))^(2) + (-8(1)/(3) - 16)^(3)}} - 4$
$x = \sqrt[3]{(114 - 2(1)/(2)) + \sqrt{(114 - 2(1)/(2))^(2) + (-24(1)/(3))^(3)}} + \sqrt[3]{(114 - 2(1)/(2)) - \sqrt{(114 - 2(1)/(2))^(2) + (-24(1)/(3))^(3)}} - 4$
$x = \sqrt[3]{(112(1)/(2)) + \sqrt{(112(1)/(2))^(2) - (24(1)/(3))^(3)}} - \sqrt[3]{(112(1)/(2)) + \sqrt{(112(1)/(2))^(2) - (24(1)/(3))^(3)}} - 4$
$x = \sqrt[3]{112(1)/(2) + √(12656.25 - 14408.037)} + \sqrt[3]{112(1)/(2) + √(12656.25 - 14408.037)} - 4$
$x = \sqrt[3]{112(1)/(2) + √(-1751.787)} + \sqrt[3]{112(1)/(2) - √(-1751.787)} - 4$
$x = \sqrt[3]{112(1)/(2) + 41.855i} + \sqrt[3]{112(1)/(2) - 41.855i} - 4$
$x = -4 + \sqrt[3]{112(1)/(2) + 41.855i} + \sqrt[3]{112(1)/(2) - 41.855i}$

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Simplify the polynomial (3a^2+4a+25) - (2a^2+4a-5)

Answers

Answer:

The polynomial simplified would be a^2 + 30

I hope this helps you:))

P.S. Might I recommend a good online calculator for these types of problems. It's called Symbolab. I use it every day and it's a lifesaver. It shows the step-by-step and has a plethora of different actions like simplifying, inverse, and line.

When flying from Florida to the Philippines island why does the shortest route pass through Alaska?

Answers

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What is the answer M divided by 3+5=2

Answers

Solve for M by simplifying both sides of the equation, then isolating the variable.M=−9

If two triangles are congruent which of the following statements must be true? CHECK ALL THAT APPLYA. The triangles have the same size but not the same shape.
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Answers

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brainly.com/question/1675117

#SPJ5

Dr. Black is standing 13 feet from a streetlamp. The lamp is making his shadow 9 feet long. He estimates that the angle of elevation from the tip of his shadow to the top of the streetlamp is 50. To the nearest foot, the streetlamp is about _____.

Answers

Distance from tip of shadow to lamp post = 13 +9 feet = 22 ft Height of lamp post = x tan 50 = x /22 = 1.192 x = 22 * 1.192 =.26.2 ft. rounded = 26ft

Answer:

26 ft height

Step-by-step explanation:

The distance between the streetlamp and the tip of his shadow is 9 + 13 = 22 ft.

A rectangle triangle is formed in which one side is 22 ft long and the other side is the streetlamp height. The angle between the 22 ft side and the hypotenuse is 50°. From tangent definition:

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Answers

Hello, Yoloalanis. In order to solve this question that you have just posted, you only have to do a few simple steps. So, We can do this!

Let's start with your fraction. You will first have to change 9/12 into a decimal. In order to do this, you will have to divide the numerator by the denominator. A numerator is also known as the top part of the fraction. A denominator is the bottom part of the fraction. So, when you divide nine by twelve, you get 0.75 as a decimal. Now, you just have to multiply the decimal by 100 or to make it simpler, just move the decimal two places to the right. To sum it all up, you will get 75%.

Hope it helps :)

$\bold{ (9)/(12)(100)} \n \n \Bigg( (9)/(12) \Bigg)\Bigg((100)/(1) \Bigg) \n \n \bigg( (3)/(4)\bigg) \bigg( (100)/(1)\bigg) \n \n \n \Bold{ ((3)(100))/((4)(1)) } \n \n (300)/(4) \n \n \boxed{\pmb{{=75}}}$

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