Question

4 problems please help, will medal best answer.
1. Determine the equation of the asymptotes: g(x) 2x^2+1/x+3 2. Use Descartes' rule of signs to describe the roots of h(x)=4x^4-5x^3+2x^2-x+5 3. Solve the polynomial equation x^3-7x^2-x+7=0 4. Solve the polynomial expression x^4+x^3-6x^2-14x-12=0

Answer 1

1. Determine the equation of the asymptotes:
g(x) 2x^2+1/x+3
2. Use Descartes' rule of signs to describe the roots of
h(x)=4x^4-5x^3+2x^2-x+5
3. Solve the polynomial equation
x^3-7x^2-x+7=0
4. Solve the polynomial expression
x^4+x^3-6x^2-14x-12=0

Answer 2

@Thegame1974

Answer 3

hang on

Answer 4

for the first one:
2x-6 with a remainder of 19/x+3
i hope this helps

Answer 5

1) set the denominator equal to zero and solve

Answer 6

2) Use Descartes' rule of signs to describe the roots of \(h(x)=4x^4-5x^3+2x^2-x+5 \) the coefficients have 4 changes in sign, from 4 to -5, from -5 to +2, from +2 to -1, from -1 to +5
therefore they may be 4, 2 or 0 positive zeros (you count down by twos)

Answer 7

now compute the change of sign of the coefficient of \[h(-x)=4x^4+5x^3+2x^2+x+5\]

Answer 8

i count none (all the coefficients are positive) , so no negative zeros