Hi again!
The zeros are the values of x. This is where the graph intersects the x - axis. In order to find the zeros, replace y with 0 and solve for x.
The answer is x = 0, -π, 4I am not sure what grade are you or the level, but for me, they sometimes asked me to find their multiplicities as well
The multiplicity of a root is the number of times the root appears.
So, the answer are
x = 0 and the multiplicity of 2
x = -π and the multiplicity of 3
x = 4 and the multiplicity of 2
Good luck with your studies!
Answer:
No complex roots; 3 real roots
Step-by-step explanation:
If a third order polynomial has any complex roots, then as a rule it has 1 real root and 2 complex roots. In this particular case, the polynomial has three real roots, as can be determined by graphing the function. The graph crosses the x-axis in 3 places.
Let's start by visualising this concept.
Number of grains on square:
1 2 4 8 16 ...
We can see that it starts to form a geometric sequence, with the common ratio being 2.
For the first question, we simply want the fifteenth term, so we just use the nth term geometric form:


Thus, there are 16, 384 grains on the fifteenth square.
The second question begs the same process, only this time, it's a summation. Using our sum to n terms of geometric sequence, we get:



Thus, there are 32, 767 total grains on the first 15 squares, and you should be able to work the rest from here.
Since there are three variables and three constants you add like terms.
3(x+15) = 3x + 40