IIT JEE , AIEEE Forum - Mathematics , Algebra

akshax

How do you solve cubic equation of the form:

ax³+ bx² + cx + d = 0

is there any formula like there is for quadratic??

madman

no there is no exact formula but u can solve it this way.
if p,q, and r are the roots then
p+q+r=-b/a
pq+qp+rp=c/a
pqr=-d/a
solving the above three equations u can get the roots
rate if useful

akshax

but then if u solve it usin this, u will again get a cubic eqn...in p q or r..!

lokeshsardana

let x1,x2,x3 be its roots
then, x1+x2+x3 = -b/a
x1x2+ x2x3 + x3x1 = c/a
x1x2x3 = -d/a

this is only we know abt equation................

rate if satisfied.............otherwise nudge me.

karthik_18049200

yes.
there is a formula
first u put x=y-b/3a
then substitute in the cubic equation
then you get the equation which do not have x² term

that is a cubic in x with co-efficient of x²=0
then if u get a cubic like this,
y³+ay=b,put b=s³-t³&a=3st(assumption)
then,u observe that,y=s-t satisfies y³+ay=b
hence s=a/3t
solve for t
then solve for s
hence u can get y
from that,u can get x
hence cubic equation is solved
please rate me

karthik_18049200

this is the exact formula for solving cubic & quatic equations also
rate me

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