8. Transform the equation 12.5 34x2 + 33x-1=0 into another which shall have the same roots with opposite signs.

9. Transform the equation 3 − 15x2 + 7x + 125 = 0 into another whose roots are less by 5.

10. Transform the equation 3 3.5 + 7.5 1.250 into another whose roots are double those of the given equation. 11. Transform the equation x3 12.2 18.+ 135 = 0 into another whose roots are of the roots of the given equation.

12. Solve the equation 3 roots are in the ratio of 3 to 2.

13. Solve the equation 3

in A. P.

--

9x14x + 24 = 0, two of whose

9x2+23x-15=0, whose roots are

15. Transform the equation x3. ax2 bx c 0 into another whose roots are the square of the roots of the given equation.

16. The equation 3.x1 25x350x2 50.c+12= 0 has two roots whose product is 2; find all the roots.

17. Show that the equation x3 - x2 - 10 has one real root only.

J

21. Find the inferior limit to the

the equation -3x2-x+1 = 0.

number of imaginary roots of

22. Find the nature of the roots of the equation + 15x2 + 7x -11

= 0.

23. Find the multiple roots of the equations:

(a) y3 + y2 — 16y+ 20 = 0.

(d) y1 — 2y3 — 11y2 + 12y + 36 = 0.

24. Determine the number and situation of the real roots of the

equations:

(a) x3 2.x2 10 = 0.

(b) x3- 9x+5= 0.

(c) 5.x3-7.x2+3x+9=0.

(d) x x19x+11= 0.

(e) x+ 2.x3 + 3x2 20.x 47 = 0.

(f)

x2+8.x3 30.x2 210.x + 241 = 0.

(g) x1 7.x3 +33x2 · 55x + 80 = 0.

Determine the real roots of the following equations by Horner's

28. 2x-12x2 + 9x + 24 = 0. Ans. 4.3098; 2.7155; -1.0253.

29. The equation 2.3

between 300 and 400; find it.

650.8x2 + 5x − 1627 = 0 has a root Ans. Commensurable root 325.4.

30. Find the root between 20 and 30 of the equation

33. 2.x1

34. 3.

35. 10.

7.x3

Ans. 2.8809; — 2.8193
Ans. 3.7509; - 3.8048.
Ans. +1;
0.4406.

0.9503; 2.0241.

4x3 + 3x2 − 1 = 0.
2x3- 21x-4x+11= 0.
Ans. 4.0071; 0.6339;
- 15x2 + 2x + 34 = 0.

Ans. 1.5055; 0.5367; 0.5397; -0.8025.

36. The equation x + 2x + 3x3 + 4x2 + 5x = 321 has one real root; find it.

Ans. 2.638605803327.