Wednesday

April 1, 2015

April 1, 2015

Posted by **edward** on Tuesday, December 20, 2011 at 8:07pm.

f(x) = 2x^4 + 19x^3 + 37x^2 - 55x - 75

- algebra -
**Damon**, Tuesday, December 20, 2011 at 8:34pmGraph this first to find the zeros, hopefully exactly.

- algebra -
**edward**, Tuesday, December 20, 2011 at 9:36pmThere is a process to this and it's why I am asking for help.

- algebra -
**Steve**, Wednesday, December 21, 2011 at 11:17amAll rational roots will have a numerator which is a factor of 75, and a denominator which is a factor of 2.

±1 ±3 ±5 ±15 ±25 ±75

±1/2 ±3/2 ±5/2 ±15/2 ±25/2 ±75/2

Descartes' Rule of Signs says that there are at most

1 positive real root

2x^4 + 19x^3 + 37x^2 - 55x - 75 has one change of sign

2 negative real roots

2x^4 - 19x^3 + 37x^2 + 55x - 75

So, we either have a double root, or some complex roots.

A little synthetic division reveals that there are no real roots greater than 2 or less than -6.

A little more produces the root -1

(x+1)(2x^3 + 17x^2 + 20x - 75)

(x+1)(2x-3)(x+5)^2

- algebra -
**DeAnn**, Thursday, April 26, 2012 at 8:45pmI have done synthetic divion and come up with 3/2 and -1 but still have not gotten it down to a trinomial.

**Answer this Question**

**Related Questions**

Rational Zeros - List all possible rational zeros for the polynomial below. Find...

Math - Possible or Potential rational zeros - List all possible (or potential) ...

Math - potential zero - List all possible (or potential) rational zeros for the ...

Math Problem2 - List all possible rational zeros for the polynomial below. Find ...

algebra - List all possible or potential rational zeros for the polynomial below...

precalculus - I'm going to do this on my own, but I would like to check mine ...

math - list all the possible rational zeros for the polynomial below. find all ...

college algebra - 1. solve the following logarithmic equation log_8(x+8)+log_8(x...

college algebra - use the rational zeros theorem to find all the real zeros of ...

Algebra - Consider the polynomial: f(x) = 2x^3 – 3x^2 – 8x – 3. (a) By using the...