Answered

Looking for answers? Westonci.ca is your go-to Q&A platform, offering quick, trustworthy responses from a community of experts. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

For the given polynomials find the sum of the squares of the roots. P(x)=x^3-x^2-18x+k

Sagot :

loneguy

[tex]\text{Given that,}\\\\P(x) = x^3 -x^2 -18x+k\\\\\text{If the roots are}~ \alpha, ~ \beta,~\text{and}~ \gamma, ~ \text{then},\\\\\alpha +\beta+\gamma= -\dfrac{(-1)}1 = 1\\\\\alpha \beta +\beta \gamma + \gamma \alpha= -\dfrac{18}1 = -18\\ \\\text{Now, sum of the squares of the roots,}\\\\\alpha^2 + \beta^2 + \gamma^2 = ( \alpha + \beta + \gamma)^2 -2(\alpha \beta + \gamma \beta + \gamma \alpha)\\ \\~~~~~~~~~~~~~~~~~~=1^2 - 2(-18)\\\\~~~~~~~~~~~~~~~~~~=1+36\\\\~~~~~~~~~~~~~~~~~~=37[/tex]

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.