1. Find in yards the side of a square whose 640 acres.

2. A square garden contains of an acre. yards the length of its side.

3. A dealer sold a suit of clothes at as mai profit as the suit cost dollars. If the profit v the prime cost of the suit of clothes.

4. The width of a rectangle is of its le area is 15 acres. Find its dimensions in ya

5. Two numbers are in the ratio of 4

product is 1620. Find them.

6. Two numbers are in the ratio of sum of their squares is 7225. Find the

7. Two numbers are in the ratio e difference of their squares is 5184. F

=

8. The area of a circle πr2, π be the radius of the circle. Calculate circle whose area is (a) 1809.6, (b) 6.

9. The surface of a sphere = 47 radius of the sphere whose surface is 6) 45,239 square inches,

CHAPTER XI

QUADRATIC EQUATIONS

123. A quadratic equation in one variable is an equation of the form ax2 + bx + c = 0, a, b, and c being known numbers or constants, a not zero.

A quadratic equation is also called an equation of the second degree.

The following are examples of quadratic equations:

x2=20.

x2-3x=0.

x2+3x-4=0.

124. A quadratic equation of the form ax2+c=0 is called an incomplete quadratic. In English text-books this form of quadratic is known as a pure quadratic.

A quadratic equation of the form ax2 + bx + c = 0, and b being different from zero, is called a complete quadratic. In English text-books a complete quadratic is generally known as an adfected quadratic. Some American texts use affected where English texts use adfected.

Example 1. Solve

5(x2-3x+1)-3(2x2 −5x+3)+20= 0.

SOLUTION. Removing parentheses,

5 x2-15x+5-6 x2+15x-9+20=0.

Combining,

-22160.

5(42 − 3 × 4+1) − 3(2 × 42 − 5 × 4 + 3) + 20 = 0.

125. Solution of quadratics by factoring.

Example 1. Find the roots of the equation

SOLUTION. Transposing 13 x, x2 - 13x+40= 0.

If either of these factors is equal to zero, the equation

is satisfied.

If

If

x-5=0, then x=5.

x80, then x 8.

The roots of x2 - 13x + 40 are 5 and 8.

Check. 52+40= 13 x 5.

82+40= 13 x 8.

To solve a quadratic equation by factoring

1. Bring all the terms to the first member of the equation. 2. Factor.

3. Make each factor equal to zero.

4. Solve the resulting simple equations.

126. Since a quadratic expression can be resolved into two factors of the first degree, a quadratic equation has two and only two roots.