**Question:**

If , , be the roots of the cubic equation . Prove that the equation in y whose roots are is obtained by the transformation . Hence, form the equation with above roots.

**Solution:**

Given that , , are the roots of the equation:

…call this equation I.

By relationships between roots and co-efficients, (Viete’s relations), we get

and , and

Now, , that is,

, or …call this equation II.

Subtracting Equation II from Equation I, we get

since

which is the required transformation.

Now, , that is,

Putting this value of x in Equation I, we get

, that is,

, which is the required equation.

Cheers,

Nalin Pithwa.

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