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Vesnalui [34]
3 years ago
5

NEED HELP AND NEED TO SHOW WORK

Mathematics
1 answer:
Olin [163]3 years ago
7 0

Answer:

f(-2) = 0

f(1) = 12

(x^3 - 7x - 6) / (x + 2) = x^2 - 2·x - 3 = (x - 3)(x + 1)

x^3 - 7x - 6 = (x + 2)(x - 3)(x + 1)

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Plss help me TT
Marina CMI [18]

a. There are 0 or 2 real positive roots for the equation and

b. There are 0 or 2 real negative roots for the equation.

<h3>What is the Descartes'rule of sign?</h3>

Descartes' rule of sign states that

  • The number of real positive zero of a polynomial f(x) is the number of sign changes of the coefficients of f(x) or an even number less than the number of sign changes of the coefficients of f(x)
  • The number of real negative zero of a polynomial f(x) is the number of sign changes of the coefficients of f(-x) or an even number less than the number of sign changes of the coefficients of f(-x)

<h3>How to find the number of possible positive and negative roots are there for the equation?</h3>

Given the equation 0 = −8x¹⁰ − 2x⁷ + 8x⁴ − 4x² − 1, writing it as a polynomial function, we have f(x) = −8x¹⁰ − 2x⁷ + 8x⁴ − 4x² − 1

<h3>a. The number of positive roots</h3>

So, to find the number of positive roots, we find the number of sign changes of the polynomial f(x).

So, f(x) = −8x¹⁰ − 2x⁷ + 8x⁴ − 4x² − 1

Since f(x) has coefficients -8, -2, + 8, -4, -1, there are two sign changes from -2 to + 8 and from + 8 to -4.

So, there are 2 or 2 - 2 = 0 real positive roots.

So, there are 0 or 2 real positive roots for the equation.

<h3>b. The number of negative roots</h3>

So, to find the number of negative roots, we find the number of sign changes of the polynomial f(-x).

So, f(-x) = −8(-x)¹⁰ − 2(-x)⁷ + 8(-x)⁴ − 4(-x)² − 1

= −8x¹⁰ + 2x⁷ + 8x⁴ − 4x² − 1

Since f(x) has coefficients -8, +2, + 8, -4, -1, there are two sign changes from -8 to + 2 and from + 8 to -4.

So, there are 2 or 2 - 2 = 0 real negative roots.

So, there are 0 or 2 real negative roots for the equation.

So,

  • There are 0 or 2 real positive roots for the equation and
  • There are 0 or 2 real negative roots for the equation.

Learn more about Descartes' rule of sign here:

brainly.com/question/28487633

#SPJ1

8 0
1 year ago
Which statement is true?
iVinArrow [24]

Answer:

the answer is " the slope of the function A is less then the slop of the function B

hope it helps

5 0
2 years ago
Read 2 more answers
Plzzz help me with numbers 6 and 10!!!!!!
sukhopar [10]

see attached picture for #6


10 the inequality would be :

 12 inch box is x

15 inch box is y

12x+15y≤84

6 0
2 years ago
Parallel lines m and n are cut by a transversal t. Which two angles are NOT corresponding angles?
Alex787 [66]
1 and 6 are not corresponding angles. They have different degrees. hope this helps :)
6 0
3 years ago
Read 2 more answers
How to graph 14x+18y=126
Burka [1]

  • We need to rearrange this into y=my+c
  • Subtract 14x from both sides
  • 18y=-14x+126
  • Divide both sides by 2
  • 9y=-7x+63
  • Divide both sides by 9
  • y=\frac{-7x+63}{9}=\frac{-7x}{9} +\frac{63}{9}
  • Plot the point (0, 63/9)
  • Then pick some x values and put them into the equation to find the respective y values
  • Then plot those points
  • Finally join up those points
4 0
2 years ago
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