Chapter 10 Section 1 Square Root Property

Learning Objectives Know that every positive real number has two square roots. Solve quadratic equation using the square root property

Key Vocabulary Quadratic Equation Square Root Property

Quadratic Equation Standard form of a quadratic equation is ax 2 + bx + c = 0 a, b, and c are real numbers and a ≠ 0 a is the coefficient of the squared term b is the coefficient of the first-degree term c is the constant It is important to label the a, b and c with the correct sign when substituting into the quadratic formula

Positive Real Numbers Every positive real number has two square roots Example

Positive Real Numbers Example

Square Root Property If x 2 = a then or written as Mostly used when an equations like x = 0 cannot be factored, however it works on all equations in this form. Solve:Difference in two squares x 2 – 49 = 0 x 2 – 7 2 = 0 (x – 7) (x + 7) x – 7 = 0 and x + 7 = 0 x = 7 and x = -7

Solve: Square Root Property

Solve:

Solve:

Solve: Square Root Property

Solve: Square Root Property

The length of a rectangle is 4.5 times the width. If the area of the rectangle is 1152 cm 2 find the length and width. Let: x = width 4.5x = length area = (length)(width) width = x = 16 length = 4.5x = 4.5(16) = 72 discard the -16 Square Root Property

The square root property is needed to solve equations like x 2 – 13 = 0 that cannot be factored When we evaluated a square root such as we found only the principle square root, 3 When using the square root property we include both the positive and the negative square root. We have to use ± sign When solving an application problem we sometimes find solutions that are not true or does not make since and we have to discard them. Remember

HOMEWORK 10.1 Page 593: # 7, 11, 17, 19, 23, 27, 29, 41