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FrozenT [24]
3 years ago
6

The sum of 4 times a number and -2 is equal to the sum of 5 times the number and -2. Find the number

Mathematics
1 answer:
MArishka [77]3 years ago
6 0
4n(-2)=(5)(-2)
-8n=-10
—— —-
-8 -8

n= 5/4
n= 1 1/4

So the final answer is n= 1.25
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I hope this helps!
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alukav5142 [94]
In this problem, we need to plug in the given x values for f(x)=0 and find a and b.

When we plug in 1, we get: 2 \times {1}^{4} - 5 \times {1}^{3} - 14 \times {1}^{2} + a \times 1 + b = 0

Simplify:
2 - 5 - 14 + a + b = 0
- 17 + a + b = 0
a + b = 17

We got our first statement about the values of the variables. If we find one more we can find those 2 variables.

We have another given root: 4.

Plug it in:
2 \times {4}^{4} - 5 \times {4}^{3} - 14 \times {4}^{2} + a \times 4 + b = 0
512 - 320 - 224 + 4a + b = 0
- 32 + 4a + b = 0
4a + b = 32

Now we have our second one. We can combine them:
a + b = 17 \\ 4a + b = 32

I use elimination method which is easier here.

Multiply the top equation by -1: - a - b = - 17 \\ 4a + b = 32

Add them up:
3a = 15

Simplify:
a = 5

Now we have a, we can plug in one of those equations to find b:
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b = 17 - 5
b = 12

So, the answers are a=5 and b=12 .
6 0
3 years ago
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