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Consider a monic cubic polynomial with and roots Find the value of ​

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Consider a monic cubic polynomial $$f(x)$$ with $$f(6)=7, f(-6)=2$$ and roots $$r,s,t$$ Find the value of $$rs+st+rt.$$

Oct 15, 2022

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$$f(x)=ax^3+bx^2+cx+d\\ a=1\\ f(x)=x^3+bx^2+cx+d\\ -b=r+s+t\\ c=rs+rt+st\\ -d=rst$$

So I am asked to find c

$$f(x)=x^3+bx^2+cx+d\\ f(6)=6^3+b*6^2+c*6+d\\ f(6)=216+36b+6c+d\\~\\ f(-6)=-216+36b-6c+d\\~\\ f(6)-f(-6)=432+12c=7-2\\ 12c=-427\\ c=35\frac{7}{12}$$

You need to check for careless errors.

Oct 15, 2022
edited by Melody  Oct 15, 2022