Elementary Algebra; Second Course Volume 1-2

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1913 edition. Excerpt: ...1. 6, 2. 3.-5, -3. 5.-7, 6. 2. 9, 1. 4. 8, -2. 6.-12, -2. satisfies the equation Ax2-j-Bx + C = 0. The graph of (1) is some kind of curve, and the graph of (2) is the: r-axis (see 51). Hence, since the coordinates of the points where the graphs of (1) and (2) cross must satisfy both (1) and (2) (see 53), the roots of Ax" + Bx + C= 0 may be obtained by observing the adistances of the points where the graph of (1) (rosses the #-axis. For another method of solving a quadratic graphically, see First Course, pages 292 and 293. Example.--Solve graphically x2-11 x + 24 = 0. Let y = x2-Ux + 24. By assigning values to x, and computing the corresponding values of y, the following sets of values are obtained: Locating the points whose coordinates are these sets of values of x and y, and connecting them by a smooth line, gives the curve on the preceding page. It is seen that this curve crosses the z-axis at two points, A and li, whose z-distances are 3 and 8, respectively. Hence, the roots of x2-11 x + 24 = 0 are 3 and 8. If the roots of a quadratic are equal, the graph of (1) will just touch the o-axis at one point. Example.--The roots of x2--14 x 4-49 = 0 are each + 7. The graph of y = x2 14 x + 49 is the curve (a) in the figure, which just touches the z-axis at a point whose z-distance is the root 4-7. If the roots of a quadratic are imaginary, the graph of (1) will not cross or touch the x-axis at all. Example.--The roots of x2-4 x + 8 = 0 are 2 2 i. The graph of y = x2-4x + & is the curve (6) in the figure, which lies entirely above the E-axis. Find, by the discriminant, the nature of the roots of the following, and give their graphical interpretation: 7. 4x2-33a; + 8 = 0. 10. a? + x + 5 = 0. 8. 22 + 3a; = 54. 11. 9ar-a; + 2 =...show more

Product details

• Paperback | 44 pages
• 189 x 246 x 2mm | 95g
• Miami Fl, United States
• English
• black & white illustrations
• 123661450X
• 9781236614506