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alekssr [168]
2 years ago
13

The polynomial equation x^4 + x^3 + x^2 + x + 1 = 0 has zero positive real roots. Please select the best answer from the choices

provided T F
Mathematics
1 answer:
const2013 [10]2 years ago
5 0

There are zero positive real roots for the given polynomial equation x^4 + x^3 + x^2 + x + 1 = 0. This is explained by Descarte's rule of signs. So, the best choice is T (true).

<h3>What is Descarte's rule of signs?</h3>
  • Descarte's rule of signs tells about the number of positive real roots and negative real roots.
  • The number of changes in signs of the coefficients of the terms of the given polynomial f(x) gives the positive real zeros of the polynomial.
  • The number of changes in signs of the coefficients of the terms of the given polynomial when f(-x) gives the negative real zeros of the polynomial.

<h3>Calculation:</h3>

The given polynomial equation is x^4 + x^3 + x^2 + x + 1 = 0

On applying Descarte's rule of signs,

f(x)=x^4 + x^3 + x^2 + x + 1

Since there are no changes in the signs of the coefficients of any of the terms in the above polynomial, the polynomial has no positive real roots.

f(-x)=(-x)^4+(-x)^3+(-x)^2+(-x)+1\\      = x^4-x^3+x^2-x+1

Since there are four changes in the signs of the coefficients of the terms of the given polynomial when f(-x), the polynomial has 4 negative real roots.

Therefore, the given polynomial equation has zero positive real roots. So, the correct choice is T(true).

Learn more about Descarte's rule of signs here:

brainly.com/question/11590228

#SPJ1

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Plz i need this done quick thx
eduard

Answer:

106 degrees

Step-by-step explanation:

Sides AB and CD are equal in length and sides AD and BC are parallel to each other. This tells us that angles B and C are equivalent. Knowing this, we can set up the following equation to solve for x:

4x+42=74+2x

Subtract both sides by 42

4x+42-42=74+2x-42\\4x=32+2x

Subtract both sides by 2x

4x-2x=32+2x-2x\\2x=32

Divide both sides by 2

\frac{2x}{2} =\frac{32}{2} \\x=16

Now, to find angle ABC, or angle B, we can plug x back into its expression:

4x+42\\= 4(16)+42\\=64+42\\= 106

Therefore, the measure of angle ABC is 106 degrees.

I hope this helps!

5 0
3 years ago
Twice the quantity b plus 9
mojhsa [17]

Answer:

2b+9

Step-by-step explanation:

Twice the quantity b is 2*b = 2b

...and then you add 9 which is:

2b+9

5 0
3 years ago
H(a) = 2a+ 5g(a) = 3a−5Find h(a)+ g(a)
Alexandra [31]

Answer:

5a

Step-by-step explanation:

h(a) = 2a+ 5

g(a) = 3a−5

h(a)+g(a)

(2a+5)+(3a-5) (substitution)

2a+5+3a-5 (open parentheses)

5a+0 (solve)

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7 0
2 years ago
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nikdorinn [45]
Sum of the terms of the series is

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we have n= 6 , a1= 17, an = 57
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600

Step-by-step explanation:

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8 0
3 years ago
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