Page:Elementary algebra (1896).djvu/498

480 Rh


 * +++4 |

+ +

ALGEBRA.

Ae) f@) fil)

it H+++

++HH |

3 variations. 3 variations. 2 variations. 2 variations. 2 variations. 2 variations. 1 variation.

1 variation.

1 variation.

no variation. no variation.

+++4++444444

+++++ |

Thus one root lies between — 4 and — 5; a second lies between 0 and — 1, and the third lies between 2 and 3.

EXAMPLES XLVIII. g.

Determine the number and situation of the real roots of :

. 8 —492-624+8=0.

. 24+ 1122+ 8x-—16=0.

1 2 RL = ete 7 SD, 4

§. a§—4a34+2?46x442=0. 6. at—23+x—1=0. 7. 23 — 9324 234 —16=0.

. — 4934692? -122742=0. 8 2+ 08-2024 24—-1=0.

GRAPHICAL REPRESENTATION OF FUNCTIONS.

Coordinates.

608. Two lines drawn at right angles to each other as in Fig. 1 form a simple system of lines of reference. Their

intersection, O, is called the origin. Distances from O along XX' are called abscissas; distances from XX' on a line parallel to Y'Y' are called ordinates.

609. Abscissas measured to the right of the origin are considered positive, and to the left, negative. Ordinates measured above XX' are considered positive, and when taken below XX' are negative.