The number of times that the number 4 goes into 50 is 12 which gives 48 and there will be a remainder of 2.
It is required to find the number of times that the number 4 goes into 50.
This means that the division problem has to be done by dividing the number 50 by 4.
When numbering out the multiples of 4, it is known that:
4 × 10 = 40
Then,
4 × 11 = 44
4 × 12 = 48
4 × 13 = 52
Since, 50 lies in the exact middle of 48 and 52, the number of times that 4 goes into 50 is 12.5.
Or as an integer, the number 4 goes into 50, 12 times and there will be a remainder of 2.
Hence, the number of times 4 goes into 50 is 12.
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Fifth degree polynomial; scary stuff. We know it has five complex roots, counting multiplicities. How many are real?
The rational root test tells us we only have to try the divisors of 9, so 1, -1, 3, -3, 9, -9. We find x=3 gives
243 - 243 - 54 + 54 - 9 + 9 = 0
in nice pairs.
So x-3 is a factor and we can divide to get a 4th degree polynomial. The division is a bit easier than usual.
x^4 - 2x^2 - 3
x - 3 | x^5 - 3x^4 - 2x^3 + 6x^2 - 3x + 9
x^5 - 3x^4
0 - 2x^3 + 6x^2
0 - 3x + 9
0
So we get
It's downhill from here. The new factor is really just a quadratic in x squared, and factors easily:
And now if we descend into irrational and complex numbers, we can further factor
and we can read off our roots,
We have one rational root, namely 3, and two irrational roots, the square roots of three, and two purely imaginary roots.
Answer: 1 rational, 2 irrational
Answer:
One rational and 2 irrational zeroes
Step-by-step explanation:
I agree with the other guy.
f(3) = 0 so x = 3 is a rational root.
There also are 2 irrational roots and 2 complex roots.
.
.
A. (–4, –1)
B. (–4, 0)
C. (–4, 1)
D. (–4, 2)