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

6 0

2 years ago

Find the value of x please help

dezoksy [38]

6x + 1 + 29 = 90

6x + 30 = 90

6x = 90 - 30

6x = 60

x = 60/6

x = 10

7 0

2 years ago

Home heating oil is sold by the gallon. Last winter the romano family used 370 gallons of oil at a price of $3.91 per gallon. If

shusha [124]

($3.91)(0.09) = $0.3519

$3.91 + 0.3519 = $4.2619 per gallon

if you're looking for the total expense next year:

($4.2619)(370 gallons) = $1,576.903

6 0

3 years ago