### MCQ's collected from all Engineering Entrance Examinations (Click here)

### Important Formulas :

1. If are real or complex numbers then is called a quadratic expression in and is called a quadratic equation. If are all rational, then is called a rational quadratic equation.

2.A real or complex number is said to be a root or solution of the quadratic equation if

3.The roots of the quadratic equation are

4. is called the discriminate of the of the quadratic equation .

5.If are the roots of the quadratic equation , then and

6.The quadratic equation whose roots are and is

7.If is irrational and if is a root to the rational quadratic equation, then is also a root.

8.If is a root of the real quadratic equation, then is also a root.

9.If are real and , then the nature of the roots of equation is as follows: If , then the roots are real and distinct

10.If are real and , then the nature of the roots of equation is as follows: If , then the roots are real and equal. In this case each root is equal to then , and is called the double root or a repeated root

11.If are real and , then the nature of the roots of equation is as follows: If , then the roots are two non-real conjugate complex numbers.

12.If are rational and , then the nature of the roots of equation is as follows: If , and is perfect square then the roots are rational and distinct.

13.If are rational and , then the nature of the roots of equation is as follows: If , is not a perfect square then the roots are conjugate surds (irrationals.)

14.If are rational and , then the nature of the roots of equation is as follows: If , then the roots are rational and equal.

15.If are rational and , then the nature of the roots of equation is as follows: If , then the roots non-real conjugate complex numbers.

16.If are rational and , then the nature of the roots of equation is as follows: If , and is a perfect square, then the roots are integers.

17.Relation between the roots of , where , are real. .

18.Relation between the roots of , where , are real.

19.Relation between the roots of , where , are real.

20.Relation between the roots of , where , are real. if

21.Relation between the roots of , where , are real.

22.Relation between the roots of , where , are real.

23.Relation between the roots of , where , are real.

24.Relation between the roots of , where , are real.

25.Relation between the roots of , where , are real.

26.Relation between the roots of , where , are real.

27.Relation between the roots of , where , are real.

28.Relation between the roots of , where , are real.

30.Relation between the roots of , where , are real.

31.Relation between the roots of , where , are real

32.Relation between the roots of , where , are real

33.For any quadratic equation , If and are of the same sign, then product of roots is the roots have the same sign.

34.For any quadratic equation , If and are of opposite signs , then product of roots is the roots will have opposite sign

35.For any quadratic equation , If both the roots are then will have the same sign.

36.For any quadratic equation , If the two roots are then will have the same sign different from the sign .

37.For any quadratic equation , If .then the roots are reciprocal to each other [product of the roots is 1]

38.For any quadratic equation , If . then the sum of the roots is equals to zero [the roots have the same absolute value i.e., the roots are in the form ]

39.For any quadratic equation , If then the roots are and

40.For any quadratic equation , If i.e., then the roots are and .

41.For any quadratic equation , If one root is zero then .

42.For any quadratic equation , If are integers and the roots are rational numbers, then these roots must be integers.

43.For any quadratic equation , If the roots are in the ratio , then .

44.For any quadratic equation , If one root is ,times the other , then .

45.For any quadratic equation , If one root is equal to the , power of the other root then

46.For any quadratic equation , If one root is the square of the otherthen .

47.For any quadratic equation , If and have the same roots then

48.For any quadratic equation , If the equations and have a common root then and the common root is

49.If the equation , has non real complex roots , then and will have the same sign .

50.If the equation , has equal rootsthen and have the same sign .

51.If the equation , has real roots and then and are of opposite sign.

52.If the equation , has real roots and then and have the same sign.

for_QUODRATIC-EQUATIONS