MAT 1330 Lecture Notes - Lecture 5: Quadratic Equation

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1330
• Professor: Rachelle Miron

Document Summary

Goal: recall and practice all the high-school material that you will need for this course. Algebraic manipulations ii: simplify multiple fractions, rationalize a denominator: simplify 4+ 1 k 2, rationalize the denominator k. Polynomials: solve quadratic equations, factor a polynomial, long division m + 6: solve 1 x + 1 x2 = 1, solve m , solve 4x. 1+x = 3x: factor x3 + 1000, divide x3 + x2 + 5. 2 3 > 5: easy: x, harder 2 x 3 > 5, solve |x2 5| = 1. 2 3| > 5: solve | x. Check out the history and applications of the quadratic equation on https://plus. maths. org/content/os/issue29/features/quadratic/index. Question 1: simplify the following expressions. (cid:0)x1/2y1/3(cid:1) 1/2 x2y3 (a) (cid:0)x1/2y1/3(cid:1) 1/2 x3y2 (b) (c) x3/4y3 x 1/4y. 1 (b) a 1 + x 2 a 2 x 1 (c) Question 5: find all solutions of the following equations. Question 7: find all solutions of the following equations. (a) 3x +