Question
Solve the equation in the real number system
X^4+11x^3+24x^2-23x+35=0
Please show work
X^4+11x^3+24x^2-23x+35=0
Please show work
Answers
Damon
the 35 tempts me to try -7 and -
divide mess by (x+5)
get
(x+5)(x^3+6x^2-6x+7)
so divide
(x^3+6x^2-6x+7) by (x+7)
get
(x+5)(x+7)(x^2-x+1)
now that last one has no real roots
b^2-4ac = 1-4 = -3
so our only real roots are
(-5,0) and (-7,0)
divide mess by (x+5)
get
(x+5)(x^3+6x^2-6x+7)
so divide
(x^3+6x^2-6x+7) by (x+7)
get
(x+5)(x+7)(x^2-x+1)
now that last one has no real roots
b^2-4ac = 1-4 = -3
so our only real roots are
(-5,0) and (-7,0)