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Quadratic Equations and Functions

Find the known root w = -5, subtract it from the total sum 37/3 to find the second root, then solve for a directly in Desmos.

18(w - a)(w + 5) = 6(w + 5) In the given equation, a is a constant. The sum of the solutions to the equation is \frac{37}{3}. What is the value of a?

Answer: 17

Nov 7, 08:40 PMView Solution →

Quadratic Equations and Functions

Graph y = x^2 + (q - 2)x + 55 with a slider for q, or graph the inequality (q - 2)^2 - 220 < 0 to visually find the largest integer upper bound.

Math Difficulty: Hard r^2 + qr = 2r - 55 In the given equation, q is an integer constant. The given equation has no real solutions. What is the largest possible value of q?

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Solved Questions Archive

Find the known root w = -5, subtract it from the total sum 37/3 to find the second root, then solve for a directly in Desmos.

Graph y = x^2 + (q - 2)x + 55 with a slider for q, or graph the inequality (q - 2)^2 - 220 < 0 to visually find the largest integer upper bound.

Define the factored polynomial h(x) = (x + 5)(x - 6)(x - 7) in Desmos and evaluate h(0) to find the constant term c.

Use the axis of symmetry x = 10: since x = 8 and x = 12 are both 2 units away from the vertex price, the number of bowls sold at $8 must equal the number sold at $12 (5 bowls).

Identify the contextual definitions of the coordinates: x is unit price and y is revenue, meaning an x-intercept (a, 0) corresponds to a unit price producing $0 revenue.