1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Helga [31]
3 years ago
14

Find all real zeros of 4x^3-20x+16

Mathematics
2 answers:
Pani-rosa [81]3 years ago
5 0

Answer:

  {1, (-1±√17)/2}

Step-by-step explanation:

There are formulas for the real and/or complex roots of a cubic, but they are so complicated that they are rarely used. Instead, various other strategies are employed. My favorite is the simplest--let a graphing calculator show you the zeros.

___

Descartes observed that the sign changes in the coefficients can tell you the number of real roots. This expression has two sign changes (+-+), so has 0 or 2 positive real roots. If the odd-degree terms have their signs changed, there is only one sign change (-++), so one negative real root.

It can also be informative to add the coefficients in both cases--as is, and with the odd-degree term signs changed. Here, the sum is zero in the first case, so we know immediately that x=1 is a zero of the expression. That is sufficient to help us reduce the problem to finding the zeros of the remaining quadratic factor.

__

Using synthetic division (or polynomial long division) to factor out x-1 (after removing the common factor of 4), we find the remaining quadratic factor to be x²+x-4.

The zeros of this quadratic factor can be found using the quadratic formula:

  a=1, b=1, c=-4

  x = (-b±√(b²-4ac))/(2a) = (-1±√1+16)/2

  x = (-1 ±√17)2

The zeros are 1 and (-1±√17)/2.

_____

The graph shows the zeros of the expression. It also shows the quadratic after dividing out the factor (x-1). The vertex of that quadratic can be used to find the remaining solutions exactly: -0.5 ± √4.25.

__

The given expression factors as ...

  4(x -1)(x² +x -4)

Rzqust [24]3 years ago
4 0

Answer:

Step-by-step explanation:

You might be interested in
Bill and Pete shared 1/2 of a cake. Bill got to eat twice as much cake as Pete. What fraction of the whole cake did Bill eat?
KatRina [158]

Answer:

Step-by-step explanation:

Total cake shared=1/2

Pete share=x

Bill= twice as much as Pete

=2x

Pete's share+ Bill's share=total share

x+2x=1/2

3x=1/2

x=1/2÷3

x=1/2×1/3

=1/6

Pete's share=x=1/6

Bill's share=2x

=2(1/6)

=2/6

=1/3

3 0
3 years ago
A) Simplify<br> X-2<br> 7(x - 2)2
Finger [1]

Answer:

welp-

7(x - 2)2 = 14(x-2) = 14x-28

I hope this helps:)

-♥

6 0
2 years ago
On December 13, 2007, one British pound was worth 2.04 U.S. dollars.
Alika [10]

Answer:

a) 5 pounds

b) 365 dollars

3 0
1 year ago
Question 10 pls help
Ivenika [448]

Answer:

D

Step-by-step explanation:

3 0
2 years ago
The perimeter of a bedroom is 88 feet. The ratio of the width to the length is 5:6. What are the dimensions of the bedroom?
Elza [17]

Answer:

20 feet wide, 24 feet long

Step-by-step explanation:

Let x - width, y - length.

The perimeter is given by the formula:

P = 2*(width + length) or using x, y

P = 2*(x + y) = 88

x + y = 44

And we know that the ratio between the sides is 5/6:

x/y = 5/6. x is on top because the length is bigger than the width

x = 5y/6

Plug this in the first expression:

y + 5y/6 = 44. Muliply by 6

6y + 5y = 264

11y = 264

y = 264/11 = 24.

So x = 5(24)/6  = 20

7 0
3 years ago
Other questions:
  • Plz help with question
    13·1 answer
  • F(x)= (x - 6)(x + 2)?<br> What is the vertex of the quadratic function
    7·1 answer
  • A new club sent out 172 coupons to boost sales for next year's memberships. They provided 3 times as many to potential members
    5·1 answer
  • I really need help with the question someone give me the answer please
    11·2 answers
  • Point A is located at (-5, 2) on a coordinate grid. Point A is translated 4 units to the right and 2 units down to create point
    9·1 answer
  • Tell whether the angles are adjacent or vertical. Then find the value of x.
    10·1 answer
  • Write the conditional statement that the venn diagram illustrates.
    7·1 answer
  • Help lol i need it rn
    12·1 answer
  • The function f is defined by the following rule.
    6·1 answer
  • Yo i need help just with the answer to rounding 418,832 to the nearest ten thousand.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!