How many solutions over the complex number system does this polynomial have? 7x^5-33x^4-4x^2+3x+52=0

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.

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500

good luck on your studies! : )

david edward.