What are the rational roots of the polynomial f(x)=20x4+x3+8x2+x-12

The rational root theorem tells you they will be of the form ...

... ±(divisor of 12)/(divisor of 20)

Hence any rational root will be one of ...

... {±1/20, ±1/10, ±3/20, ±1/5, ±1/4, ±3/10, ±2/5, ±1/2, ±3/5, ±3/4, ±4/5, ±1, ±6/5, ±3/2, ±2, ±12/5, ±3, ±4, ±6, ±12}

A graph shows them to be -4/5 and +3/4.

_____

Dividing (5x+4) and (4x-3) from f(x) gives a quotient of (x²+1). Since there are only two real zeros, we already know the remaining roots are complex. This factor tells us they are 1±i.

1     sepan

2     encuentren

3     tenga

4     hable

5   parezca

6   llegue

no oblique asymptote

step-by-step explanation:

to find the oblique asymptote of f(x)

here numerator has degree 1 and denomintor degree 2

degree of numerator < degree of denominator

hence there is no oblique asymptote

when the degree of the denominator > that of the numerator, we saw that the value in the denominator got so much bigger, so quickly,   giving us a horizontal asymptote of the x-axis. or we can write

f(x) = a polynomial of x + a proper fraction.

in this case only we have oblique asymptotes but not when numerator has less degree.