For a positive integer n, the complex number z = r(cos 0 + i sin 0) has exactly n distinct nth roots given by vr(cos 0 + 2rk COS 0 + 2xk + i sin in in where k = 0, 1, 2, . ..,n – 1. Use the formula above to find all the solutions of the equation and represent the solutions graphically. x3 – 729 = 0 k = 0: k = 1: k = 2:

Q: Find the discriminate of each quadratic equation then state the number and type of solutions.

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Q: Solve for all values of x by factoring. x2 – 2x – 12 = –2x + 4 -

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Q: Solve for the indicated variable. (x+8k)(x-5)=x² +8x-40k, for k

A: To solve for the indicated variable.

Q: Solve for x for all real solutions: 8x2 - 9x + 15 = 0

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Q: 5. Find all real solutions of the equation: 2x +7x -8x2 - 25x-6 0 1

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.