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spin [16.1K]
3 years ago
10

Which values are possible rational roots of 4x3+9x2−x+10=0 according to the rational root theorem? Select each correct answer. ±

12 ±2 ±52 ±25
Mathematics
2 answers:
chubhunter [2.5K]3 years ago
4 0

Answer:

±2

Step-by-step explanation:

For simplicity let's take a look at a general third order polynomial:

ax^3 + bx^2 + cx + d.  In this particular case,

rational roots have the form ±d/±a.  Note that these are fractions/ratios.  Beyond that, we factor d and choose numerators ±(all possible whole number factors of d, dividing these results by all possible factors of a.

Looking at 4x^3 + 9x^2 - x + 10 = 0, we see that d = 10 and that factors of d include ±1, ±2, ±5 and ±10.  a = 4 and factors of a include ±1, ±2, ±4.

So, any rational roots of the given polynomial will stem from the possible rational roots

±1    ±2    ±5    ±10    ±1    ±2    ±5    ±10

--- , ----- , -----, ------- , ---- , ----- , --- , ------ , and so on,

±1    ±1     ±1      ±1      ±2    ±2   ±2     ±2

until you have used up all of the possible factors of 10 and all of the possible factors of 4.  

Of the four possible rational roots you have shared, only ±2 (which would actually be ±2 / ±1) is acceptable.

zavuch27 [327]3 years ago
3 0

Answer:

the answer would be +_ 2

Step-by-step explanation:


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PLEASE ANSWER WITH AN EXPLANATION! THANK YOU
lubasha [3.4K]

Answer:

\large\boxed{A=153\ cm^2}

Step-by-step explanation:

<em>Look at the picture.</em>

We have

square with side length a = 9

trapezoid with base lengths b₁ = 9 and b₂ = 6 and the height length h = 6

right triangle with legs lengths l₁ = 3 + 6 = 9 and l₂ = 6

The formula of an area of a square

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Substitute:

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The formula of an area of a trapezoid:

A=\dfrac{b_1+b_2}{2}\cdot h

Substitute:

A_{II}=\dfrac{9+6}{2}\cdot6=\dfrac{15}{2\!\!\!\!\diagup_1}\cdot6\!\!\!\!\diagup^3=(15)(3)=45\ cm^2

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A=\dfrac{l_1l_2}{2}

Substitute:

A_{III}=\dfrac{(9)(6)}{2}=\dfrac{54}{2}=27\ cm^2

The area of the shape:

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