1. ## Quadratic and cubic equation -show that -(common roots)

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

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

how to show a=b=c??

2. ## Re: Quadratic and cubic equation -show that -(common roots)

Originally Posted by sumedh
If the equations ax^2+bx+c=0 and x^3+3x^2+3x+2=0 have two common solutions then show a=b=c.

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

how to show a=b=c??
This means that $ax^2+bx+c$ is a factor of $ax^3+3ax^2+3ax+2a$. Perform polynomial long division and set the remainder to zero.

(this process give the required solution and one other solution, but the second solution when checked is a spurious solution)

CB

3. ## Re: Quadratic and cubic equation -show that -(common roots)

can we solve by the following formulas

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?

4. ## Re: Quadratic and cubic equation -show that -(common roots)

thank you very much i got it