Quadratic and cubic equation -show that -(common roots)

[Sumedh]

Homework Statement

If the equations ax²+bx+c=0 and x³+3x²+3x+2=0 have two common solutions then show a=b=c.

Homework Equations

The Attempt at a Solution

first equation will be the factor of second.
taking out common from first equation.


how to show a=b=c??
please provide hints.

 

[SammyS]

Find a real root of the cubic equation. Write the cubic polynomial as the product of a quadratic factor and a linear factor.

 

[PeterO]

Homework Statement

If the equations ax²+bx+c=0 and x³+3x²+3x+2=0 have two common solutions then show a=b=c.

Homework Equations

The Attempt at a Solution

first equation will be the factor of second.
taking out common from first equation.how to show a=b=c??
please provide hints.

factorise the cubic.

 

[uart]

The easiest way to approach this is to divide (x^3 + 3x^2+ 3x + 2) by (x^2 + x +1) to prove that it's a factor. You don't actually need to factorize, just verify that the factor.

 

[Sumedh]

can we solve by the following formulas

for quadratic eqs.
α+ß =-b/a

αß= c/a

for cubic equations
(Γ=gamma)

α+ß+Γ=-b/a

(αß)+(ßΓ)+(αΓ)=c/a

αßΓ=-d/a



i am trying to solve by this method but i hung up! in between?

 

[Sumedh]

thank you very much i got it