Quadratic Equations Questions and Answers

Quadratic Equations Questions

Formula

Definition of Quadratic Equations

Quadratic Equation is an equation which contains at least one squared term. It can be defined in the form of rx^2 + dx + z = 0. Where a, b and c are constants and ‘x’ is an unknown variable.

Rules

  • If p+ √q is a root of a quadratic equation, then its other root is p- √q
  • When D ≥ 0, then rx^2+ dx + z can be expressed as a product of two linear factors.
  • If α and β are the roots of rx^2+ dx + z, then we can write it as: x^2 – (α + β)x + α β = 0

Question 1

Time: 00:00:00
Calculate the number of real roots of the quadratic equation f(a)= a2+5a+6= 0? 

7

7

1

1

4

4

None

None

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Question 2

Time: 00:00:00
Calculate the number of roots of the equation a4+a2+1= 0.

2

2

-3

-3

-2

-2

None

None

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Question 3

Time: 00:00:00
Calculate the number of distinct real roots of the equation p11+7p3-5=0.

-3

-3

1

1

-6

-6

2

2

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Question 4

Time: 00:00:00
Calculate the value of p when the equation a2-(p+6) a+2(2p-1)= 0 if the total of roots equals half their product?

7

7

-7

-7

1

1

zero

zero

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Question 5

Time: 00:00:00
Calculate the least value of a if the total of squares of roots of equation p2-(a-2)p – a -1= 0? 

-4

-4

1

1

6

6

5

5

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Question 6

Time: 00:00:00
Which of the below option will be true if the equation a2+2(m+1)a+9m-5= 0?

m≥ 2

m≥ 2

m≥ -6

m≥ -6

m≥ -4

m≥ -4

None

None

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Question 7

Time: 00:00:00
Calculate the sum of roots of the below mentioned quadratic equation:

3a^{2}+2a-1= 0.

−2/3

−2/3

1/4

1/4

7/3

7/3

-5/6

-5/6

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Question 8

Time: 00:00:00
Calculate the product of roots of the below mentioned quadratic equation:

3a^{2}+2a-1= 0.

2/3

2/3

zero

zero

-1/3

-1/3

1/7

1/7

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Question 9

Time: 00:00:00
What will be the roots of the equation p2m2+pqm= q2 where p≠0

Real

Real

Not real

Not real

Real but unequal

Real but unequal

None of the above

None of the above

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Question 10

Time: 00:00:00
Which of the following values satisfies the equation -a2+6a-8>0

4

4

2

2

A<6 and a>8

A<6 and a>8

2

2

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Question 11

Time: 00:00:00
For what value of p , equation 2a+3b= 5 and 4a+pb= Q will not have any solution?

1

1

Zero

Zero

2

2

6

6

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Question 12

Time: 00:00:00
IF p and q are the roots of the equation b2-13b+f= 0 and p-q= 3 then calculate the value of f.

40

40

71

71

74

74

53

53

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Question 13

Time: 00:00:00
If a<0 then calculate the maximum value of 9/a + a/9?

-5

-5

-2

-2

4

4

-9

-9