Find all the real zeros of the polynomial. Use the quadratic formula if necessary.

Question

1. P(x)=x³+4x² +3x -2
2. P(x)=x⁴-6x³+4x²+15x+4

please show steps for both problems if there is any.

Answer 1

1) using the rational zero theorem we know that if there is a rational zero it could be 1,2,-1or-2

using synthetic division -2 is a zero so (x-2) is a factor with the remaining fact being x^2 +2x -1. This expression does not factor so need to use quadratic formula to get the other factors which are

(-1+sqroot 2) and (-1-sqroot2)

so your zeros are x=2, and 1+/- ssroot2