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