Page:Elementary algebra (1896).djvu/514

496 Rh 8. x^3+x-3=0; root between 1 and 2. 9. x^3+2x-20=-0; root between 2 and 3. 10. x^3 + 10x^2+ 8x - 120 =0; root between 2 and 3. 11. 3x^3+ 5x -40=0; root between 2 and 8. 12. x^4 - 12x^2+ 12x-3=0; root between - 3 and - 4. 13. x^5 - 4x^4 + 7x^3 - 863 = 0; root between 4 and 5.

Find the real roots of the following equations :

14. x^3-3x-1=0. 16. x^4- 8x^3 + 12x^2 + 4x-8=0. 15. x^3 - 22x -24=0. 17. x^4+ x^3+ x^2 + 3x -100=0.

Find to four decimals, by Horner’s Method, the value of the following :

18. 3 11. 19. 4 13 20. 5 5. 21. 5 7

MISCELLANEOUS EXAMPLES VII.

1. Simplify b - {b -(a + b)-[b -(b -a - b)] + 2 a}. 2. Find the sum of a+b-2(c+d), b+c-3(d+a) and c+d-4(a+b). 8. Multiply {1}{2}+ {2}{3}y by x-{1} {3}y. 4. If x=6, y=4, z=3, find the value of 2x+3y+z. 5. Find the square of 2- 3x + x^2. 6.Solve {x+3}{x-1} + {x-4}{x-6} =2. 4. Find the H.C.F. of a^3 -2a-4 and a^3 - a^2 -4. 8. Simplify {2a}{a+b} + {2b}{a-b} - {a^2 +b^2}{a^2 -b^2} 9. Solve {3}{5}x + {y}{} = \\ {1}{3} x - {y}{8} = 3

10. Two digits, which form a number, change places when 18 is added to the number, and the sum of the two numbers thus formed is 44: find the digits. 11. a = 1, b = -2, c=3, d=- 4, find the value of {a^2b^2 + b^c+ d(a-b)}{10a-(c+b)^2}