1. The condition for polynomial equation a$x^2$ + bx + c = 0 to be quadratic is

2. The number of real solutions of the equation ${\left|x\right|}^2-3\left|x\right|$+2 = 0 is

3. The equation x + 1/x = 2$x^2$ has a root x = 1, therefore, it will have

4. If a, b are non real roots of a$x^2$ + bx + c = 0 (a, b, c $ϵ$ R), then

5. The roots of (x – a) (x – b) = ab$x^2$ are always

6. The equation (b - c) $x^2$ + (c – a) x + (a –b) = 0 has

7. Both the roots of the equation a$x^2$ + bx + c = 0, a $\ne$ 0, are zero if

8. If a$x^2$ = bx + c = 0 is satisfied by every value of x, then

9. Roots of $x^2$ + k = 0, k < 0 are

10. If the roots of a$x^2$+ b = 0 are real and distinct then

11. If the product of the roots of the equation m$x^2$+ 6x + (2m – 1) = 0 is -1, then the value of m

12. If a > 0, b > 0, c > 0, then the roots of the equation a$x^2$ + bx + c = 0 are

13. If a, b are odd integers, then the roots of the equation 2a$x^2$ + (2a + b)x + b = 0 are

14. The quadratic equation 8 ${\sec }^2$θ – 6 sec$\theta$ + 1 = 0 has

15. If one root of the equation a$x^2$+ bx + c = 0, a $\ne$ 0, be reciprocal of the other, then

16. If the roots of a$x^2$ + bx + c = 0 are equal in magnitude but opposite in sign, then

17. If a, b are the roots of the equation $x^2$ - 2x + 2 = 0, then the value of $a^2$ + $b^2$ is

18. If a, b are the roots of a$x^2$ + bx + c = 0, the roots of c$x^2$ + bx + a = 0 are

19. The number of real roots of the equation $2^2$$x^2$ - 7x + 5 = 1 is

20. The roots of the equation $x^2$ + ax + b = 0 where a = 2$\sqrt{b}$ and b > 3 are

21. If x = a is one of the factors of the polynomial a$x^2$ + bx + c, then one of the roots of a$x^2$ + bx + c = 0 is

22. If one root of the equation $x^2$ + px + 12 = 0 is 4 while the equation $x^2$ + px + q = 0 has equal roots, the value of q is

23. If the root of equation $\frac{a}{x-a}$ + $\frac{b}{x-b}$ =1 are eqal in magnitude and oppositing sign then,

24. The numerical difference of the roots of $x^2$ - 7x – 9 = 0 is

25. The value of p and q (p$\ne$ 0, q$\ne$ 0) for which p, q are the roots of the equation $x^2$+ px + q = 0 are

26. If a + b + c = 0, a $\ne$ 0, a, b, c $ϵ$ Q, then both the roots of the equation a$x^2$ + bx + c = 0 are

27. If the roots of the equation 12$x^2$ + mx + 5 = 0 are in the ratio 3:2, then m equals

28. If a, b, c are positive real numbers, then the number of real roots of the equation

28. a$x^2$+b$\left|x\right|$+c= 0 is

29. The values of x which satisfy both the equations $x^2$-1≤ 0 and $x^2$ - x – 2 ≥ 0 lies in

30. Ram and sham solved a quadratic equation. In solving it Ram made a mistake in the constant term only and got the roots as 8 and 2, while sham made a mistake in the co-efficient of x only and obtained -9 and -1 as roots. The correct roots of the equation are

31. If a non-zero root of the equation $x^2$ + 2x + 3$\lambda$ = 0 and 2$x^2$ + 3x + 5$\lambda$ = 0 is common, then the value of $\lambda$ will be

32. If a and b are the roots of $x^2$ + px + q = 0 and $a^4$, $b^4$ are the roots of x²$x^2$ - rx + s = 0, then the equation $x^2$ - 4 qx + 2q² - r = 0 has always

33. If the roots of $x^2$ - bx + c = 0 are two consecutive integers, then $b^2$ - 4c is

34. Let the equation a$x^2$ - bx + c = 0 have distinct real roots both lying in the open interval (0, 1) where a, b, c are given to be positive integers. Then the value of the ordered triplet (a, b, c) can be

35. The condition that $x^3$ - p$x^2$ + qx – r = 0 may have two of its roots equal to each other but of opposite signs is

36. All the integral values of x for which 7x – 3 >${(x+1)}^2$> x + 3 lie in the interval

37. The solution set of the equation $|5x-3|$ = -1 is

38. if x, y $ϵ$ R, xy rational, y irrational and x rational, then

39. If x $ϵ$ R, then $x^2$ + x + 2

40. If x and y are real numbers such that x > y and $\left|x\right|$< $\left|y\right|$, then;

41. If 2 – 3x – 2 $x^2\ge$ 0, then,

42. Irrational numbers are;

43. If x be a positive real, then the least value of x + 1/x is

44. If x is a non-zero rational number and xy is irrational, then y must be

45. If a,b are the roots of $x^2$ - 2x + 4 = 0, then a/b is equal to