Question

Question is there below

Answer 1

Answer:

$-\frac{bc}{a^{2} }$

Step-by-step 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 ↓

$\alpha +\beta =-\frac{b}{a}$

$\alpha \beta =\frac{c}{a}$

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,

= $\frac{c}{a} (-\frac{b}{a} )$

= $-\frac{bc}{a^{2} }$

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