How do you find the rational roots of #x^4+5x^3+7x^2-3x-10=0#?
Use the rational roots theorem to find rational roots
The rational roots theorem tells us that all rational roots of
So the possible rational roots are:
Note that the sum of the coefficients of
We also find
We can long divide
A quick check of the discriminant of this quotient polynomial finds:
So there are no more real roots and no more linear factors with real coefficients.