Question #16058

use matlab to find the roots of 13x^3+182x^2-184x+2503=0

Expert's answer

to obtain an exact solution run the following commands:

syms x;

q=solve('13*x^3+182*x^2-184*x+2503', x)

This will give the

following three roots:

q =

- 3100/(117*(162109/702 -

(79092^(1/2)*2746509413^(1/2))/79092)^(1/3)) - (162109/702 -

1/79092*79092^(1/2)*2746509413^(1/2))^(1/3) - 14/3

1550/(117*(162109/702 -

(79092^(1/2)*2746509413^(1/2))/79092)^(1/3)) + (162109/702 -

(79092^(1/2)*2746509413^(1/2))/79092)^(1/3)/2 -

(3^(1/2)*i*(3100/(117*(162109/702 - (79092^(1/2)*2746509413^(1/2))/79092)^(1/3))

- (162109/702 - 1/79092*79092^(1/2)*2746509413^(1/2))^(1/3)))/2 -

14/3

1550/(117*(162109/702 - (79092^(1/2)*2746509413^(1/2))/79092)^(1/3))

+ (162109/702 - (79092^(1/2)*2746509413^(1/2))/79092)^(1/3)/2 +

(3^(1/2)*i*(3100/(117*(162109/702 - (79092^(1/2)*2746509413^(1/2))/79092)^(1/3))

- (162109/702 - 1/79092*79092^(1/2)*2746509413^(1/2))^(1/3)))/2 -

14/3

The formulas are rather complicated.

To obtain numerical

solutions use the commands

syms x;

q=solve('13*x^3+182*x^2-184*x+2503.0', x)

Then we get the following

numerical values of roots:

q =

-15.684996994758873743020093097571

3.400812098166834260546246531635608088941016256759685592753500752*i +

0.8424984973794368715100465487855931052563643471910202548058171968

0.8424984973794368715100465487855931216471495813440972869080880358 -

3.4008120981668342605462465316356*i

syms x;

q=solve('13*x^3+182*x^2-184*x+2503', x)

This will give the

following three roots:

q =

- 3100/(117*(162109/702 -

(79092^(1/2)*2746509413^(1/2))/79092)^(1/3)) - (162109/702 -

1/79092*79092^(1/2)*2746509413^(1/2))^(1/3) - 14/3

1550/(117*(162109/702 -

(79092^(1/2)*2746509413^(1/2))/79092)^(1/3)) + (162109/702 -

(79092^(1/2)*2746509413^(1/2))/79092)^(1/3)/2 -

(3^(1/2)*i*(3100/(117*(162109/702 - (79092^(1/2)*2746509413^(1/2))/79092)^(1/3))

- (162109/702 - 1/79092*79092^(1/2)*2746509413^(1/2))^(1/3)))/2 -

14/3

1550/(117*(162109/702 - (79092^(1/2)*2746509413^(1/2))/79092)^(1/3))

+ (162109/702 - (79092^(1/2)*2746509413^(1/2))/79092)^(1/3)/2 +

(3^(1/2)*i*(3100/(117*(162109/702 - (79092^(1/2)*2746509413^(1/2))/79092)^(1/3))

- (162109/702 - 1/79092*79092^(1/2)*2746509413^(1/2))^(1/3)))/2 -

14/3

The formulas are rather complicated.

To obtain numerical

solutions use the commands

syms x;

q=solve('13*x^3+182*x^2-184*x+2503.0', x)

Then we get the following

numerical values of roots:

q =

-15.684996994758873743020093097571

3.400812098166834260546246531635608088941016256759685592753500752*i +

0.8424984973794368715100465487855931052563643471910202548058171968

0.8424984973794368715100465487855931216471495813440972869080880358 -

3.4008120981668342605462465316356*i

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