Question
List all possible rational zeros for the polynomial below. Find all real zeros of the polynomial and factor
f(x)=2x^4+19x^3+37x^2-55x-75
f(x)=2x^4+19x^3+37x^2-55x-75
Answers
I tried ±1, ±3, ±5
found -1 and -5 to be zeros
So after synthetic division by x+1 and x+5
I got
2x^4+19x^3+37x^2-55x-75 = (x+1)x+5)(2x^2 + 7x - 15)
= (x+1)(x+5)(x+5)(2x - 3)
so we have a double zero at -5, and zeros at -1 and 3/2
found -1 and -5 to be zeros
So after synthetic division by x+1 and x+5
I got
2x^4+19x^3+37x^2-55x-75 = (x+1)x+5)(2x^2 + 7x - 15)
= (x+1)(x+5)(x+5)(2x - 3)
so we have a double zero at -5, and zeros at -1 and 3/2
any possible rational zeroes would have a numerator which divides 75 and a denominator which divides 2. So, the list would be
±1 ±3 ±5 ±15 ±25 ±75
±1/2 ±3/2 ±5/2 ±15/2 ±25/2 ±75/2
±1 ±3 ±5 ±15 ±25 ±75
±1/2 ±3/2 ±5/2 ±15/2 ±25/2 ±75/2
DERRRR
Related Questions
List all possible (or potential) rational zeros for the polynomial below. Find all real zeros of the...
List all possible rational zeros for the polynomial below.
Find all real zeros of the polynomial...
List all possible or potential rational zeros for the polynomial below find all real zeros of the po...