SOLUTION: x^3+4x^2+7x+28=0 find possible rational roots: find possible actual roots:

Question 701630: x^3+4x^2+7x+28=0
find possible rational roots:
find possible actual roots:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Possible Rational Roots: List all the factors of 28

Possible Rational Roots: 1, 2, 4, 7, 14, 28, -1, -2, -4, -7, -14, -28

Note: make sure you list the negative factors as well

Another Note: This trick only works if the leading coefficient is 1 or -1.
------------------------------------------------------------------------

Actual Roots:

x^3+4x^2+7x+28=0

(x^3+4x^2)+(7x+28)=0

x^2(x+4)+7(x+4)=0

(x^2+7)(x+4) = 0

x^2+7 = 0 or x+4 = 0

x^2 = -7 or x = -4

x = sqrt(-7), x = -sqrt(-7), or x = -4

x = i*sqrt(7), x = -i*sqrt(7), or x = -4

The actual roots are x = i*sqrt(7), x = -i*sqrt(7), or x = -4

The first two are complex or imaginary roots. The third root is real and rational.

The only actual rational root is x = -4

RELATED QUESTIONS
x^3+4x^2+7x=28=0 find possible rational roots: find possible actual roots:... (answered by jim_thompson5910)

Use the Rational Root Teorem to list all possible rational roots. Then find any actual... (answered by robertb)

Use the rational root theorem to list all possible rational roots for each equation.then... (answered by KMST)

list all rational zeros use synthetic division to test the possible rational roots and... (answered by shorty4aboo)

Use the Rational Root Theorem to list all possible rational roots of the polynomial... (answered by solver91311)

Use the Rational Root Theorem to list all possible rational roots of the polynomial... (answered by jsmallt9)

Use the Rational Root Theorem to list all possible rational roots for each equation. Then (answered by robertb)

Use the Rational Root Theorem to list all possible rational roots for each equation. Then (answered by stanbon)

Find the solution set: x^3+x^2-7x-3 Hint: the possible rational roots are factors of... (answered by josgarithmetic)