Question

if alpha and beta are zeroes of polynomial ax²+bx+c then evaluate alpha²/beta + beta²/alpha​

Answer 1

Answer:

If alpha and beta are the zeros of polynomial a X square +bx +c, what is Alpha square upon beta +beta square upon alpha?

I don’t know how useful this is, but the answer is:

This works as follows:

By the quadratic formula, the two zeroes of a quadratic are given by:

and

So, if we let α be one of the zeroes, and β be the other zero, then we can substitute the above expressions and solve.

First, a bit of simplifying:

And using sum of cubes, you can factorise this to:

Now, you can take each part of the expression and, by substitution, you can work out a simpler expression in a, b, c. To summarise:

And:

And:

Okay, so if you substitute these values for the different parts and simplify, you’ll get the final answer.

Obviously, I’m just giving you the key points here, and you’ll still need to do the substitutions to make it work, but hopefully, it gives you a sense of what you need to do.