How many solutions over the complex number system does this polynomial have? 7x^5-33x^4-4x^2+3x+52=0
2 answers:
Answer:
Over the complex number there exist two roots.
Step-by-step explanation:
Given : Polynomial
To find : How many solutions over the complex number system does this polynomial have?
Solution :
Descartes' rule of sign is used to determine the number of real zeros of a polynomial function.
Let
Now, for positive roots write the sign of f(x) and note the changes,
f(x)=+ - - + + i.e, from + to - and - to + two times sign changes.
So, Two positive roots.
Now, for negative roots write the sign of f(-x) and note the changes,
f(-x)=- - - + + i.e, from - to + one time sign changes.
So, One negative roots.
Since, The polynomial is of 5 degree so five roots exist.
i.e, rest two roots are complex.
Therefore, Over the complex number there exist two roots.
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This question is solved using a system of equations, and doing this, we get that: There are 9 quarters, 4 nickels and 12 dimes.
I am going to say that:
x is the number of nickels.
y is the number of dimes.
z is the number of quarters.
In all, they are worth $3.65.
A nickel is worth $0.05, a dime is worth $0.1 and a quarter is worth $0.25, so:
Dimes: 3 times greater than nickels:
This means that:
Quarters: One greater than double the number of nickels:
This means that:
Value of x:
We have y and z as function of x, so we can replace into the equation and find the value of x, so:
y and z:
There are 9 quarters, 4 nickels and 12 dimes.
A similar question is found at brainly.com/question/17096268