3 years ago

The value of a boat, in dollars, x years after its purchase is represented by the function.

Mathematics

1 answer:

valentinak56 [21]3 years ago

5 0

I believe it is 44 because u can add them and get that

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

slega [8]

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