The roots of the equation x^2+bx+c=0 are −4 and 2. Find b and Find c

1 answer:

5 0

Since its roots are -4 and 2 and a = 1 [The coefficient of x^2] we know that x^2 + bx + c = (x - (-4)) (x-2)=(x+4)(x-2) = 0. Using the distributive property we get, x^2 + 2x - 8 = 0. By equating coefficients (common strategy for partial fractions and undetermined coefficient method of solving ODE), we get b = 2 and c = -8.

Hope this helps :) If you spot a mistake in my work or have a question comment down below.

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A community theater uses the function p (d) = (-4d+40) (d−40) to model the profit (in dollars) expected in a weekend when the ti

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The theater make the maximum profit at d = $25. Then the maximum profit of the theatre is $ 900.

<h3>What is differentiation?</h3>

The rate of change of a function with respect to the variable is called differentiation. It may be increasing or decreasing.

A community theater uses the function P(d) = (− 4d + 40) (d − 40) to model the profit (in dollars) expected on a weekend when the tickets to a comedy show are priced at d dollars each.

Then the maximum profit of the theatre will be

The function is P(d) = (− 4d + 40) (d − 40)

Differentiate the function with respect to d and put it equal to zero for maximum or minimum profit.

$\begin{aligned} \dfrac{\mathrm{d} }{\mathrm{d} d}P(d) &= 0\\\\\dfrac{\mathrm{d} }{\mathrm{d} d}(- 4d + 40) (d - 40) &= 0\\\\(-4d+40) -4 (d-40) &= 0\\\\-8d + 200 &= 0\\\\d &= 25 \end{aligned}$

Then the checking for maximum or minimum, again differentiate, we have

$\begin{aligned} \dfrac{\mathrm{d} }{\mathrm{d} d}P(d) &= \dfrac{\mathrm{d} }{\mathrm{d} d}(- 4d + 40) (d - 40) \\\\\dfrac{\mathrm{d} }{\mathrm{d} d}P(d) &= \dfrac{\mathrm{d} }{\mathrm{d} d}(-8d + 200) \\\\\dfrac{\mathrm{d} }{\mathrm{d} d}P(d) &= -8\\\\ \dfrac{\mathrm{d} }{\mathrm{d} d}P(d) & < 0\end{aligned}$