Answer:
Step-by-step explanation:
1) x² + 6x + 11 = 0
a = coefficient of x² = 1
b = coefficient of x = 6
c = Constant = 11
Roots = (-b ± √b² - 4ac)/2a
Roots =
2) 2x² - 16x = 50
Divide the whole equation by 2
x² - 8x = 25
Divide the coefficient of x (i. e 8 ) by 2 = 8/2 = 4, Now add 4 to both sides of the equation
x² - 8x + 4 = 25 + 4
x² - 2*4*x + 2² = 29
(x - 2)² = 29
Take square root both side
Answer:
Maximum profits are earned when x = 64 that is when 64 units are sold.
Maximum Profit = P(64) = 2,08,490.666667$
Step-by-step explanation:
We are given the following information:, where P(x) is the profit function.
We will use double derivative test to find maximum profit.
Differentiating P(x) with respect to x and equating to zero, we get,
Equating it to zero we get,
We use the quadratic formula to find the values of x:
, where a, b and c are coefficients of
respectively.
Putting these value we get x = -100, 64
Now, again differentiating
At x = 64,
Hence, maxima occurs at x = 64.
Therefore, maximum profits are earned when x = 64 that is when 64 units are sold.
Maximum Profit = P(64) = 2,08,490.666667$