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
Tamiku [17]
3 years ago
7

What are all of the real roots of the following polynomial? f(x) x^4-24x^2-25

Mathematics
2 answers:
Delicious77 [7]3 years ago
4 0

Answer:

The real roots are  ±5

Step-by-step explanation:

It is given that,

f(x) = x^4 - 24x^2 - 25

<u>To find the real roots</u>

Let x^4 - 24x^2 - 25 = 0 ----(1)

Take y = x^2

Then eq (1) becomes,

y^2 - 24y - 25 = 0

By using splitting method we can write,

y^2 + y - 25y - 25 = 0

y(y + 1) - 25(y +1) = 0

(y + 1)(y - 25) = 0

(x^2 + 1 )(x^2 - 25) = 0

From (x^2 + 1 ) we get complex roots

x^2 = -1

x = √-1

x - 25 = 0 we get real roots

x = 25

x = ±5

Therefore the real roots are  ±5

Greeley [361]3 years ago
3 0

<u>Answer:</u>

x = ±5

<u>Step-by-step explanation:</u>

We are given the following polynomial function and we are to find all of its real roots:

x^4-24x^2-25

Let y=x^2 so we can now write it as:

y^2-24y-25

Factorizing it to get:

(y^2+y)+(-25y-25)

y\left(y+1\right)-25\left(y+1\right)

\left ( y + 1 \right ) \left ( y - 2 5 \right)

Substitute back y=x^2 to get:

\left ( x^2 + 1 \right ) \left ( x^2 - 25 \right )

\left ( x^2 + 1 \right ) \left ( x + 5 \right ) \left ( x - 5 \right )

The quadratic factor has only complex roots. Therefore, the real roots are x = ±5.

You might be interested in
Someone help?!.........
koban [17]
Answer: y = -2x + 16

Explanation:

Use point slope form:

(y1 - y) = m(x1 - x)

y1 = 6 and x1 = 5 and m = -2

6 - y = -2(5 - x)
6 - y = -10 + 2x
-y = 2x - 10 - 6
-y = 2x - 16
y = -2x + 16
5 0
3 years ago
If y=6 when x=2 over 3 find x when y=12
AlexFokin [52]

Answer:

4/3 or 1 1/3

Step-by-step explanation:

So if y = 6, when x = 2/3. Then, x would equal 1 and 1/3, because 12 is twice the amount of 6, so you'd also multiply 2/3 by 2.

(To multiply a whole number by a fraction, first multiply the whole number by the numerator and then divide that by the denominator. For example: 2 × 2 = 4, since you can't really divide 4 by 3 it would stay as is, but you can turn it to a mixed number. 4/3 is the same as 1 whole and an extra 1/3, or in other words 1 1/3).

Hope this helped :)

6 0
2 years ago
732,178+167-542,137=
madreJ [45]
( 732,178 + 167 ) = 899,178
899,178 - 542,137 = *357,041 that's the last result.
3 0
3 years ago
Read 2 more answers
What is the slope of the line shown
pantera1 [17]

Answer:

a

Step-by-step explanation:

cause you go up 14 and over 6 then you divid by 2 and get 7/3

5 0
2 years ago
Read 2 more answers
Please help asap
djverab [1.8K]

Answer:

come fast in English classhshshshdhhhdhhshdhdbb

shhshshsh

5 0
2 years ago
Read 2 more answers
Other questions:
  • 32, 28, 21, 31, 18<br><br> Is 18 an outlier or no?
    12·2 answers
  • Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning.
    15·1 answer
  • The temperature in degrees Celsius can be expressed by the function c(f)=5/9(f-32) where f is the temperature in degrees farenhe
    7·2 answers
  • The state of wyoming has roughly the shape of a rectangle that is 3.6 x 102 miles long and 2.8 x 102 miles high. what is the app
    11·2 answers
  • John buys a $5,000 savings bond with a fixed interest rate of 3% with 10 years to maturity. He also buys two $5,000 zero coupon
    11·1 answer
  • Draining a half cylinder tank. A trough is shaped like a half cylinder with length 5 m and radius 1 m. the tank is full of water
    10·1 answer
  • Express each ratio as a unit rate. Round to the nearest tenth, if necessary.
    5·1 answer
  • END OF UNIT MATH TEST PLEASE HELP
    6·1 answer
  • Question 1
    6·1 answer
  • Hows everyone's day? free 25 points btw ;D
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!