I had this question:
"Find the cubic equation whose roots are twice the roots of the equation $3x^3 - 2x^2 + 1 = 0$"
In my first attempt, I solved it through the use of simultaneous equations, where I let the cubic equation be: $x^3 + bx^2 + cx + d$. However, I've been told that there is a more efficient method for higher degree polynomials - and it has been labelled as "The Substitution method".
It involved something like "Let $y = x^2$" then form a new equation using that. Could someone solve this question and explain how to do it for me?
Any help would be greatly appreciated, thanks!
The solution with the substitution method worked like this:
Let $y=2x$, $x=y/2$ then it was substituted back into the given equation.
Can someone explain this?