SOLUTION: I'm trying to find all rational zeros of the following polynomial and then find the irrational zeros. using the Rational Zeros Theorem, the Upper and Lower Bounds Theorem, Descart

Question 33788This question is from textbook College Algebra
: I'm trying to find all rational zeros of the following polynomial and then find the irrational zeros. using the Rational Zeros Theorem, the Upper and Lower Bounds Theorem, Descartes' Rule of Signs, the quadratic formula, or other factoring techniques:
P(x) = 2x^4 + 15x^3 +31 x^2 + 20x + 4
Thank You very much! This question is from textbook College Algebra

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
I'm trying to find all rational zeros of the following polynomial and then find the irrational zeros. using the Rational Zeros Theorem, the Upper and Lower Bounds Theorem, Descartes' Rule of Signs, the quadratic formula, or other factoring techniques:
P(x) = 2x^4 + 15x^3 +31 x^2 + 20x + 4
THERE ARE NO CHANGE OF SIGNS.HENCE THERE ARE NO POSITIVE REAL ROOTS
P(-X)=2X^4-15X^3+31X^2-20X+4
THERE ARE 2 CHANE OF SIGNS.HENCE THERE COULD BE MAIMUM 2 NEGATIVE REAL ROOTS.
NOW POSIBLE ROOTS ARE FACTORS OF CONSTAN TERM /FACTORS OF X^4..THAT IS...
-1/1,-2/1,-4/1,-1/2
WE FIND THAT P(-2)=0 AND P(-0.5)=0...HENCE X+2 IS A FACTOR AND X+0.5 IS A FACTOR..DIVIDING WE GET
-2|.......2.......15.........31.........20..........4
..|.......0.......-4........-22........-18.........-4
---------------------------------------------------------
-0.5|.....2.......11.........9..........2...........0
....|.....0.......-1........-5.........-2
-------------------------------------------------------------
..........2.......10.........4..........0
HENCE QUOTIENT IS...
2X^2+10X+4...OR...
P(X)=(X+2)(X+0.5)2(X^2+5X+2)=(X+2)(2X+1)(X^2+5X+2)
ROOTS OF X^2+5X+2=0....ARE GOT USING QUADRATIC FORMLA

.LET US CLL THEM A AND B..THEN
P(X)=(X+2)(2X+1)(X-A)(X-B)
RELATED QUESTIONS
Hello, My question is 2x^4+15x^3+31x^2+20x+4 find all rational zeros of the... (answered by josgarithmetic,ikleyn)

Using Rational Zero Theorem- Find all rational zeros of the polynomial... (answered by jim_thompson5910)

Find the possible rational zeros, and then find all the zeros of the polynomial function: (answered by rothauserc)

Find the possible rational zeros and then find all the zeros of the polynomial function:... (answered by josgarithmetic)

Find the possible rational zeros and then find all the zeros of the polynomial function:... (answered by greenestamps)

Find the rational zeros of the polynomial. List any irrational zeros correct to two... (answered by ewatrrr)

List all possible rational zeros of f using the rational zero theorem. Then find all the... (answered by nyc_function)

How should I start this problem? Find all rational zeros of the polynomial, and then... (answered by Boreal,josgarithmetic)