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MrRa [10]
2 years ago
7

Student scored in the 83rd

Mathematics
1 answer:
melamori03 [73]2 years ago
5 0

Answer:b

Step-by-step explanation:

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If f(1) = 0, what are all the roots of the function f(x)=x^3+3x^2-x-3? Use the Remainder Theorem.
Sophie [7]
There's no if about it, 

f(x)=x^3+3x^2-x-3


has a zero f(1)=0 so x-1 is a factor.   That's the special case of the Remainder Theorem; since f(1)=0 we'll get a remainder of zero when we divide f(x) by x-1.

At this point we can just divide or we can try more little numbers in the function.  It doesn't take too long to discover f(-1)=0 too, so  x+1 is a factor too by the remainder theorem.  I can find the third zero as well; but let's say that's out of range for most folks.

So far we have 

x^3+3x^2-x-3 = (x-1)(x+1)(x-r)

where r is the zero we haven't guessed yet.  Again we could divide f(x) by (x-1)(x+1)=x^2-1 but just looking at the constant term we must have

-3 = -1 (1)(-r) = r

so

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

We check f(-3)=(-3)^3+3(-3)^2 -(-3)-3 = 0 \quad\checkmark

We usually talk about the zeros of a function and the roots of an equation; here we have a function f(x) whose zeros are

x=1, x=-1, x=-3

8 0
2 years ago
Read 2 more answers
What is 126/6 simplified to​
MissTica

Answer: 21

Step-by-step explanation:

The reason why it's 21 because when you divide 126/6 you get a whole number instead of a mixed number.

7 0
2 years ago
Read 2 more answers
Nicole has used 6 feet of ribbon.This represents 3/8 of the total amount of the ribbon she started with. How much ribbon did Nic
GalinKa [24]
3/8x=6. x=6*8/3. x=2*8. x=16. Nicole started with 16 feet of string.
5 0
3 years ago
Jerome is going to draw a marble from the bag shown below, replace it, and then draw another marble. What is the probability tha
alexira [117]
Marbles in a bag: 3 green, 4 yellow, 5 blue, 8 pink.

Event A - get a green or yellow marble
Event B - get a pink marble

Events A and B are independent because we draw a marble from a bag with 20 marbles in both cases.
P(A)= \frac{3+4}{3+4+5+8}= \frac{7}{20}  
\\P(B)= \frac{8}{3+4+5+8}= \frac{8}{20} = \frac{2}{5}

Probability of combined events is 
P(A) \times P(B)=\frac{7}{20} \times \frac{2}{5} =\frac{7}{50}
7 0
3 years ago
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Round each number to the nearest tenth.
andreev551 [17]

Answer:For the first one 26.73 would turn into 27 and 89.42 would stay 89


Step-by-step explanation: Any number that is 5 or greater can be used to round any number.


7 0
3 years ago
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