problem in finding quad. eqn. from the roots

In general, if α(alpha) and ß (beta) are roots of eqn. ax^2 +bx +c=0

then for finding the equation whose roots are α+2 and ß+2 can be done by

addition of roots (α+2+ß+2=-b/a) and product of roots (α+2)(ß+2)=c/a

By solving this we get ax^2 -(4a-b)x + (4a-2b+c)=0

The problem is this that,by replacing x in place of (x-2)in the given equation

ax^2 +bx +c=0 we get the same answer ax^2 -(4a-b)x + (4a-2b+c)=0

but this method ( replacing x by (x-2) ..) is not mentioned anywhere

i am not able to understand this method

please help .

Re: problem in finding quad. eqn. from the roots

You can write every quadratic equation in terms of its roots, .

The roots of are and .

So

and .

So for a quadratic which has as its roots, the equation is

Expand this out.

Re: problem in finding quad. eqn. from the roots

thank you very much i got it