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.
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 .