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
finlep [7]
3 years ago
6

What is the possible number of positive and negative real roots or zeroes in f(x)=x^3+x^2-4

Mathematics
1 answer:
Tanya [424]3 years ago
3 0

This is a third degree polynomial, so we know that the maximum amount of roots will be 3.

We also know that imaginary roots come in pairs, so there is either 0 or 2 imaginary roots.

We can tell the amount of positive / negative roots by applying Descartes' rule of signs.

Let's examine the polynomial: x^3 + x^2 - 4

Note the sign changes.

From left to right, there is one sign change.

We now know there is only one positive real root.

Now, we can replace all values of x with -1 and then simplify. The number of sign changes will tell us the amount of negative roots.

(-1)^3 + (-1)^2 - 4

-1 + 1 - 4

From left to right, there are two sign changes, which tells us there will be 2 or 0 negative roots.

If there are 2, they are not imaginary.

If there are 0, they are imaginary.

<h3>So, our guaranteed root is:</h3><h3>1 positive, real root.</h3><h3>And our possible roots are:</h3><h3>2 negative, real roots.</h3><h3>0 negative, real roots, but 2 imaginary roots.</h3>
You might be interested in
Please Help me solve: 7/8 * 1/4<br> Please give your answer in simplest form, Thank You!
alukav5142 [94]
Make them the same demonatator so 7/8 times 2/8 which equals 14 over 8 for a mixed number of 1 6/8
7 0
3 years ago
Look at pic help meeeeeeeeeeeeeeeeee
VikaD [51]

Answer:

iM SORRY I DONT KNOW TRY 1/3

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
C.126<br> D.115<br> Geometry math question no Guessing and Please show work
MakcuM [25]

140 - 90 = 50

50/140 = 45/FE

FE = 140 * 45 / 50

FE = 126

Answer

C.126

4 0
3 years ago
How do you factor the polynomial 2y^2=2 times pi times y
babunello [35]

Answer:ker3q4ofj3owiklf

Step-by-step explanation:

443r

43

r

43

r

34

r34r

43

4 0
3 years ago
Please help me <br>is importe ​
Simora [160]

Answer:

22.6

Step-by-step explanation:

srry if its wrong im pretty sure its right tho good luck <3

5 0
3 years ago
Other questions:
  • The area of a trapezoid is 39 square millimeters. The height of the trapezoid is 8 millimeters. One of the base lengths of the t
    12·1 answer
  • The average weight of a 7-year old girl is 49 pounds. The average weight of an 11 year old girl is 77 pounds.
    5·1 answer
  • Write an equation for the line that passes through (8,6) and (-8,2)​
    6·1 answer
  • Solve 3 and get 70 pts
    5·2 answers
  • How to work out 5-[5+8÷4-1]
    10·2 answers
  • NEED CORRECT ANSWER PLEASE! THANKS:)
    10·1 answer
  • 4 times a number is greater than -48.what are the possible values for the number ?
    15·1 answer
  • In a topographical map of a city, the vertices of the city limits are A(10,9),B(18,9),C(18,2),D(14,4.5),E(10,4.5). The coordinat
    12·1 answer
  • Review the steps of the proof of the identity
    7·1 answer
  • The quadrilaterals JKLM and PQRS are similar.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!