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s2008m [1.1K]
3 years ago
12

The polynomial of degree 5, P(x) P(x) has leading coefficient 1, has roots of multiplicity 2 at x=5 and x=0, and a root of multi

plicity 1 at x=−1
Find a possible formula for P(x)
Mathematics
1 answer:
Savatey [412]3 years ago
7 0

Answer:

P(x) = x^5 -9x^4 + 10x^3 + 25x^2

Step-by-step explanation:

The given degree of the polynomial P(x)  = 5

The leading coefficient = 1

So, the general form of the polynomial  with degree 5 isx^5 + bx^4 + cx^3 + dx^2 + ex + f

Now root x =5 is of multiplicity 2, x = 0 of multiplicity 2, x = -1 of multiplicity 1

If x = a is the zero of the polynomial of multiplicity m, then ,(x-a)^m is the factor of the polynomial.

⇒(x-5)^2 is a factor of P(x)

(x-0)^2is another factor of P(x)

  (x +1) is the last factor of P(x)

So, P(x) = Product of all factors = (x-5)^2 (x)^2(x+1)

Solving the above expression , we get

P(x) = (x^2 + 25 -10x) (x^3 + x^2)  = x^3(x^2 + 25 -10x) +x^2(x^2 + 25 -10x) \\= x^5 + 25 x^3 -10x^4 + x^4 +25x^2 -10x^3 \\=x^5 -9x^4 + 10x^3 + 25x^2

Hence,  P(x) = x^5 -9x^4 + 10x^3 + 25x^2

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Write the equation of a line through points (5,5) and (1, 0) in point-slope form?
algol [13]

Answer:

Step-by-step explanation:

I’m assuming that the equation is to be written in slope intercept form (y=mx+b), so for this, you want to find the slope and y-intercept. To find the slope, use the equation in picture 1.

0 - 5 = -5

1 - 5 = -4

-5 / -4 = 1.25

So m, or the slope, is equal to 1.25.

To find the y-intercept, make a table like the second picture. Choose one of the ordered pairs as the given. I used 1,0.

0,?

1,0

Now find the change in x, which in this case, is 1. Then set up something like picture three.

1.25/1 = ?/1

?=1.25

Now backtrack to get:

0, -1.25

1, 0

Now we know what is y when x is 0, we know the y intercept and can make the equation:

y = 1.25x - 1.25

5 0
2 years ago
A cargo truck weighs 8750 lb the weight limit for a certain bridge is 5 tons how many pounds of cargo can be added to the truck
Vaselesa [24]

Answer:

1,250 lbs

Step-by-step explanation:

There are 2,000 in 1 ton, so 5 * 2,000 = 10,000 lbs weight limit for the bridge.

10,000-8750 = 1,250 lbs can be added to the truck  before they reach the bridge weight limit.

7 0
3 years ago
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Adrian sells handmade puppets for $10 apiece. One puppet gets damaged, so Adrian sells it for $6, resulting in a loss of $4. He
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It would be a loss of 4 dollars.
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3 years ago
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What is the absolute value of 15-7 - the absolute value of 14-6
Mice21 [21]

BRAINLIEST PLEASE!!!

Answer:

0

Step-by-step explanation:

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|8|-|8|

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4 0
3 years ago
ade wants to verify that the expression 5(3x – 6) is equivalent to 15x – 30. She substitutes 2 into each expression and evaluate
Scorpion4ik [409]

She will know if 5(3x - 6) is equivalent to 15x - 30 if they end up to be equal to the same number.


5(3x - 6)    Substitute 2 into x

5(3(2) - 6)

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15x - 30

15(2) - 30

30 - 30 = 0


They both equal 0 when 2 is substituted in, so they are equivalent.


Also if you distributed 5 into (3x - 6) it would equal 15x - 30

5 0
3 years ago
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