Student Name Institution Affiliation Course Name Instructor Name Quadratic equation This equation involves the products or multiplication of two values and one of them or both maybe zero. Such that a*b=0; Example 1 In this example ax^2 + bx + c = 0 where a and b are numeric constants of the + 7w – 21 = 0 w(w – 3) + 7(w - 3) = 0 w = -7 or 3 ( length cannot be negative therefore width = 3cm and length 3 + 4 = 7cm) . Work cited Halmos P R editor. Problem Books in Mathematics. University of Toronto examinations (1859-1865) [...]
Following are 28 types of equations, inequalities, procedures, and application problems. Choose one topic that has not already been chosen. Start a new thread, with the title indicating the number of the question you are answering. (You will receive no credit for choosing one that has already been attempted.) Write a numbered, step-by-step, procedure on how to solve the equation or inequality or how to set up and solve the type of application problem described. You may use an example in your response or just generically explain. A person new to this type of problem should be able to use your steps to solve it. Your explanation should include the final form for the solution(s) to your equation or inequality, i.e., set notation (braces) for discrete solutions or interval notation for inequalities. Types of Equations and Inequalities: Linear equation (include explanation of conditional equation, identity, and contradiction). Solving for a variable in a "literal" equation. A motion problem (distance = rate x time) A simple interest problem with two rates of interest. A mixture problem. A problem involving temperature conversion from Celsius to Fahrenheit and vice versa. Include a procedure to determine the temperature at which the two scales are equal. How to simplify the quotient of two imaginary numbers. How to raise the imaginary unit i to a large power such as 44, 99, or 67 (these are only examples; please explain the process). A quadratic equation solved by factoring. A quadratic equation solved by square root property (include rationale for why you would choose to solve it this way). A quadratic equation solved by completing the square. A quadratic equation solved by quadratic formula. A "geometric" word problem solved by Pythagorean Theorem. A "geometric" word problem involving area of a rectangle that is solved by a quadratic equation. A rational equation. A radical equation with square roots. Make sure to include the rationale behind testing every solution to make sure it is valid. A radical equation with a cube root. An equation that is "quadratic in form" and is solved by "u substitution." A linear inequality. A "three part" inequality. A quadratic inequality. Make sure to include "test values" in your explanation. A rational inequality.Make sure to include "test values" in your explanation. An absolute value equation such that when the absolute value is isolated, the other side of the equation is positive. An absolute value equation such that when the absolute value is isolated, the other side of the equation is zero or negative (explain both). An absolute value inequality starting with a < or ≤ sign. An absolute value inequality starting with a > or ≥ sign. Using an absolute value inequality to represent a situation involving the word "within." Using an absolute value inequality to represent a situation involving the words "at most."