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.
.
.
Since ABCD is parallelogram these rules apply:
Since this implies that
The answer is D.
Hope this helps.
r3t40
A. Prove that QR ≅ QR by reflexive property
Nikki is going to use SSS Property, which is Side, Side, Side. This means that, given two pairs of sides are congruent, you will have to find out the last side, which is the same side. This means that it is congruent with itself (since both triangles share the same side), and uses the reflexive property.
hope this helps
Answer: A is the correct answer
Step-by-step explanation:
Question:
-6 = n/2 - 10
Steps:
1. Multiply 2 to every side for the n to get by itself
2. Simplify,
3. Then add 20 to both sides
4. Simplify,
So the answer to this question is n = 8.
Hope that helped!!!
~Serina
What is the approximate difference between the two journeys? pLEASE HELP GIVING ALL MY POINTS TO THE FIRST PERSON WHO DOES.