Question

Question is there below

Answer 1

`-(bc)/(a^(2) )`

Explanation:

We are given
`f(x)=ax^(2) +bx+c`,
`\alpha` and
`\beta` are zeros of the function. We can use the sum and product of roots. You may have come across these equations before ↓

`\alpha +\beta =-(b)/(a)`

`\alpha \beta =(c)/(a)`

Since the coefficients are already in a, b, and c's, we do not need to sub in anything else.

Now, you are asked to evaluate
`\alpha ^(2) \beta +\alpha \beta ^(2)`. The next step after finding the roots above ↑, is to factorise this equation to be solved.

`\alpha ^(2) \beta +\alpha \beta ^(2)`

=
`\alpha \beta (\alpha +\beta )`

Sub in each respective roots,

=
`(c)/(a) (-(b)/(a) )`

=
`-(bc)/(a^(2) )`

Hope this helped! Ask me if there's any part of the working you don't understand :)