Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

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]

Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.