Question

find the degree and zeroes of the ff. polynomial fxns.

1.) 32x-18+6x^2+9x^3=0
2.) x(x+5)^4(2x+1)^2(4x-5)=0
3.) (y^2+2x-15)y^2-49=0


Please answer clearly and explain the solution clearly and easy to understand. Thanks!
(guaranteed medal for a good answer)

Answer 1

Let's have a look at the first one.

The degree is the highest power of a variable in a term so that is 3.

If you test f(0) and f(1) you get a sign change from negative to positive so there is a root between 0 and 1.

To find this root you could use a root finding method like Newton-Raphson say with an initial guess of 1/2.

You can tell from the derivative that the function is increasing so the other two roots must be complex.

Answer 2

Second one.

Reading the exponents across, 1,5,7,8 so degree is 8 and there are 8 roots.

The factorization is already done so you have x=0,-5,-1/2 and 5/4 as roots with multiplicity 1,4,2,1.

Answer 3

Third one.

Polynomial in two variables with an xy term (unless that's a typo?) and solutions can only be expressed as one in terms of the other and there as many of these as you want.