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valkas [14]
3 years ago
9

Use the Rational Zero Theorem to list all possible rational zeros for the given function. f(x) = 10x^5 + 8x^4 - 15x^3 +2x^2 - 2

Mathematics
1 answer:
vagabundo [1.1K]3 years ago
5 0

Given:

The function is:

f(x)=10x^5+8x^4-15x^3+2x^2-2

To find:

All the possible rational zeros for the given function by using the Rational Zero Theorem.

Solution:

According to the rational root theorem, all the rational roots are of the form \dfrac{p}{q},q\neq 0, where p is a factor of constant term and q is a factor of leading coefficient.

We have,

f(x)=10x^5+8x^4-15x^3+2x^2-2

Here,

Constant term = -2

Leading coefficient = 10

Factors of -2 are ±1, ±2.

Factors of 10 are ±1, ±2, ±5, ±10.

Using the rational root theorem, all the possible rational roots are:

x=\pm 1,\pm 2,\pm \dfrac{1}{2}, \pm \dfrac{1}{5},\pm \dfrac{2}{5},\pm \dfrac{1}{10}.

Therefore, all the possible rational roots of the given function are \pm 1,\pm 2,\pm \dfrac{1}{2}, \pm \dfrac{1}{5},\pm \dfrac{2}{5},\pm \dfrac{1}{10}.

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Answer:

13.75 hours

Step-by-step explanation:

First, find how many km the driver can travel:

11(35)

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Then, divide this by 28 to find how many hours the driver can travel:

385/28

= 13.75

So, the driver can travel 13.75 hours

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2 years ago
200/40+15 = ??<br><br><br>helpp mee ^^ ​
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Step-by-step explanation:

200/40=5

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3 years ago
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keeping in mind that when the logarithm base is omitted, the base 10 is assumed.

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2 years ago
Raíz cuadrada de 110
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3 years ago
Find all solutions for a triangle with c=70 c=24 and a=25
Slav-nsk [51]

Answer:

see the attachments for the two solutions

Step-by-step explanation:

When the given angle is opposite the shorter of the given sides, there will generally be two solutions. The exception is the case where the triangle is a right triangle (the ratio of the given sides is equal to the sine of the given angle). If the given angle is opposite the longer of the given sides, there is only one solution.

When a side and its opposite angle are given, as here, the law of sines can be used to solve the triangle(s). When the given angle is included between two given sides, the law of cosines can be used to solve the (one) triangle.

___

Here, the law of sines can be used to solve the triangle:

A = arcsin(a/c·sin(C)) = arcsin(25/24·sin(70°)) = 78.19° or 101.81°

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3 years ago
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