What are the real zerosto the polynomial: p(x)=x^3-19x+30

Question

Please help me answer

Answer 1

p(x)=x³-19x+30.

We can guess possible zeroes by looking at the factors of 30: 2, 3, 5, 6, 10, 15.

Starting with 2, p(2)=8-38+30=0, so x=2 is a zero. Use synthetic division to reduce to a quadratic:

2 | 1 0 -19  30

     1 2    4 -30

     1 2 -15 | 0 = x²+2x-15 = (x+5)(x-3).

Therefore the zeroes are c=2, -5, 3.