3.4 Chapter 3 Quadratic Equations

x 2 = 49 Solve the following Quadratic equations: 2x 2 – 8 = 40

Solve by completing the square. x 2 – 7x = x x – 2 =0

Solve the General Form of the equation for x by completing the square. ax 2 + bx + c = 0

Draw a Graphic Organizer of the concepts we have learned so far.

The solution of the quadratic equation ax 2 + bx + c = 0 can be found by using the quadratic formula: The Quadratic Formula

Solve 2x 2 - 5x + 2 = 0. a = 2, b = -5, c = 2 x = 2 Solving Quadratic Equations Using the Quadratic Formula or

Solve x 2 - 6x + 7 = 0. Solving Quadratic Equations Using the Quadratic Formula

Solve x 2 - 5x + 7 = 0. is not defined by real numbers, then this equation has NO REAL ROOTS. Since Solving Quadratic Equations With No Real Roots

Solving Quadratic Equations With No Real Roots - Using Complex Numbers An equation such as x = 0 (x 2 = -1) has no solution in the set of real numbers. But, by extending the number system, we can give meaning to the solution of this equation. We do this by defining i with the property that: i 2 = -1 or i = √ - 1 Since there is no real number that has its square as a negative, the number i is not a real number. It cannot be expressed as a decimal and it can not be expressed as a point on the number line. For these reasons, the square roots of negative numbers are called imaginary numbers.

Solve x 2 - 6x + 13 = 0. The roots of the equation are x = 3 + 2i and x = 3 - 2i. Solving Quadratic Equations With No Real Roots = 4i