Question 972146: For the function f(x) = x3 + 3x2 – 70x – 144, f(–9) = 0, f(–2) = 0, and f(8) = 0. What are the solutions to the equation x3 + 3x2 = 70x + 144 = 0?
A)
x = –8, x = 2, and x = 9
B)
x = –9, x = –2, and x = 8
C)
x = –8, x = –2, and x = 9
D)
x = –9, x = –8, and x = –2
Answer by Edwin McCravy(20054) (Show Source):
You can put this solution on YOUR website! For the function f(x) = x3 + 3x2 – 70x – 144, f(–9) = 0, f(–2) = 0, and f(8) = 0. What are the solutions to the equation x3 + 3x2 = 70x + 144 = 0?
A)
x = –8, x = 2, and x = 9
B)
x = –9, x = –2, and x = 8
C)
x = –8, x = –2, and x = 9
D)
x = –9, x = –8, and x = –2
This is a giveaway problem to anyone who understands it.
I'll go through it to show why it is a giveaway problem:
f(x) = x3 + 3x2 – 70x – 144
f(–9) = 0
That tells us that if you plug in (-9) for x in
f(x) = x3 + 3x2 – 70x – 144, we get 0
That means that -9 is a solution to
f(x) = x3 + 3x2 – 70x – 144 = 0
Checking to make sure that he has told us the truth:
[Not necessary if we trust the problem-maker :) ]
f(-9) = (-9)3 + 3(-9)2 – 70(-9) – 144
f(-9) = -729 + 3(81) + 630 - 144
f(-9) = -729 + 243 + 630 - 144
f(-9) = 0
The problem-maker told us the truth! f(-9) = 0.
So we'll trust him to have told us the truth on the others.
------------------------------------------------
f(–2) = 0
That tells us that if we plug in (-2) for x in
f(x) = x3 + 3x2 – 70x – 144, we get 0, that is:
That means that -2 is a solution to
f(x) = x3 + 3x2 – 70x – 144 = 0
We'll trust him that the above does give 0
---------------------------------------------
f(8) = 0
That tells us that if we plug in (8) for x in
f(x) = x3 + 3x2 – 70x – 144, we get 0, that is:
That means that 8 is a solution to
f(x) = x3 + 3x2 – 70x – 144 = 0
We'll trust him that the above does give 0
---------------------------------------------
So the solutions are –9, –2, and 8
Because telling us that f(–9) = 0, f(–2) = 0, and f(8) = 0, tells
us the solutions, what values we must plug into f(x) to get 0, and since
f(x) equals to x3 + 3x2 – 70x – 144, those values in the parentheses
are what values we must plug into x3 + 3x2 – 70x – 144 to get 0.
So they have to be solutions to the equationn x3 + 3x2 – 70x – 144 = 0.
See why it's a giveaway problem? -- like "Who's buried in Grant's tomb?" :)
Edwin
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