Rational Inequalities We adapt the preceding method when an inequality involves rational expressions. We call these rational inequalities. To solve a rational inequality: a. Change the inequality symbol to…
Month: May 2014
Quadratic and Other Polynomial Inequalities
Quadratic and Other Polynomial Inequalities Inequalities like the following are called quadratic inequalities: x2 + 3x – 10 < 0, 5×2 – 3x + 2 ≥ 0. In each…
The Discriminant
The Discriminant From the quadratic formula, we know that the solutions and of a quadratic equation are given by and . The expression b2 – 4ac is called the discriminant.…
The Quadratic Formula
The Quadratic Formula The solutions of ax + bx + c = 0 are given by x = The formula also holds when a < 0. A similar…
Solving by Completing the Square
Solving by Completing the Square To solve an equation ax2 + bx + c = 0 by completing the square: a. If a ≠ 1 , multiply by so that the…
Completing the Square
Completing the Square We can solve quadratic equations like 3×2 = 6 and (x – 2)2 = 7 by using the principle of square roots. We can also…
The principal of Square Roots
The principal of Square Roots The quadratic equation 5×2 + 8x – 2 = 0 is said to be in standard form. The quadratic equation 5×2 = 2 – 8x…
Conjugates
Conjugates Conjugates of complex number are defined as follows. The conjugate of a complex of a complex number a + bi is a – bi, and the…
Powers of i
Powers of i We now want to simplify certain expressions involving powers of i. To do so, we first see how to simplify powers of i. Simplifying powers of i…
Complex Numbers Multiplication
Complex Numbers Multiplication The complex numbers obey the commutative, associative, and distributive laws. But although the property = dose not hold for complex numbers in general, it does hold…
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