Quadratic Equations Test

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Quadratic Equations Test - 2

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Weekly Quiz Competition

Question 1
3 / -1

Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x² + 8x + 4 = 0?

A
15

B
14

C
24

D
26

E
None of these

Solution

Explanation:
a/b + b/a = (a² + b²)/ab = (a² + b² + a + b)/ab
= [(a + b)² - 2ab]/ab
a + b = -8/1 = -8
ab = 4/1 = 4
Hence a/b + b/a = [(-8)² - 2(4)]/4 = 56/4 = 14.
Question 2
3 / -1

A
-3, 1

B
3, -1

C
3, -2

D
3, 2

E
None of these

Solution
Question 3
3 / -1

Find the quadratic equations whose roots are the reciprocals of the roots of 2x² + 5x + 3 = 0?

A
3x² + 5x - 2 = 0

B
3x² + 5x + 2 = 0

C
3x² - 5x + 2 = 0

D
3x² - 5x - 2 = 0

E
None of these

Solution

Explanation:
The quadratic equation whose roots are reciprocal of 2x² + 5x + 3 = 0 can be obtained by replacing x by 1/x.
Hence, 2(1/x)² + 5(1/x) + 3 = 0
=> 3x² + 5x + 2 = 0
Question 4
3 / -1

A man could buy a certain number of notebooks for Rs.300. If each notebook cost is Rs.5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook?

A
10

B
8

C
15

D
7.50

E
None of these

Solution

Explanation:
Let the price of each note book be Rs.x.
Let the number of note books which can be brought for Rs.300 each at a price of Rs.x be y.
Hence xy = 300
=> y = 300/x
(x + 5)(y - 10) = 300 => xy + 5y - 10x - 50 = xy
=>5(300/x) - 10x - 50 = 0 => -150 + x² + 5x = 0
multiplying both sides by -1/10x
=> x² + 15x - 10x - 150 = 0
=> x(x + 15) - 10(x + 15) = 0
=> x = 10 or -15
As x>0, x = 10.
Question 5
3 / -1

I. a² - 7a + 12 = 0,
II. b² - 3b + 2 = 0 to solve both the equations to find the values of a and b?

A
if a b

E
if a ≥ b

Solution

Explanation:
I.(a - 3)(a - 4) = 0
=> a = 3, 4

II. (b - 2)(b - 1) = 0
=> b = 1, 2
=> a > b
Question 6
3 / -1

I. a² - 9a + 20 = 0,
II. 2b² - 5b - 12 = 0 to solve both the equations to find the values of a and b?

A
If a b

E
If a ≥ b

Solution

Explanation:
I. (a - 5)(a - 4) = 0
=> a = 5, 4
II. (2b + 3)(b - 4) = 0
=> b = 4, -3/2 => a ≥ b
Question 7
3 / -1

I. a² + 11a + 30 = 0,
II. b² + 6b + 5 = 0 to solve both the equations to find the values of a and b?

A
If a b

E
If a ≥ b

Solution

Explanation:
I. (a + 6)(a + 5) = 0
=> a = -6, -5
II. (b + 5)(b + 1) = 0
=> b = -5, -1 => a ≤ b
Question 8
3 / -1

I. a² + 8a + 16 = 0,
II. b² - 4b + 3 = 0 to solve both the equations to find the values of a and b?

A
If a b

E
If a ≥ b

Solution

Explanation:
I. (a + 4)² = 0 => a = -4
II.(b - 3)(b - 1) = 0
=> b = 1, 3 => a < b
Question 9
3 / -1

I. a² - 2a - 8 = 0,
II. b² = 9 to solve both the equations to find the values of a and b?

A
If a b

E
If a ≥ b

Solution

Explanation:
I. (a - 4)(a + 2) = 0
=> a = 4, -2
II. b² = 9
=> b = ± 3
-2 < 3, -2 > -3, 4 > 3, 4 > -3,
No relation can be established between a and b.
Question 10
3 / -1

I. x² + 5x + 6 = 0,
II. y² + 9y +14 = 0 to solve both the equations to find the values of x and y?

A
If x < y

B
If x > y

C
If x ≤ y

D
If x = y or the relationship between x and y cannot be established.

E
If x ≥ y

Solution

I. x2 + 3x + 2x + 6 = 0
=> (x + 3)(x + 2) = 0 => x = -3 or -2
II. y2 + 7y + 2y + 14 = 0
=> (y + 7)(y + 2) = 0 => y = -7 or -2
No relationship can be established between x and y.

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Re-Attempt Weekly Quiz Competition

Quadratic Equations Test - 2

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Quadratic Equations Test - 2

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Question 1

15

14

24

26

None of these

Solution

Question 2

-3, 1

3, -1

3, -2

3, 2

None of these

Solution

Question 3

3x2 + 5x - 2 = 0

3x2 + 5x + 2 = 0

3x2 - 5x + 2 = 0

3x2 - 5x - 2 = 0

None of these

Solution

Question 4

10

8

15

7.50

None of these

Solution

Question 5

if a < b

if a ≤ b

if the relationship between a and b cannot be established.

if a > b

if a ≥ b

Solution

Question 6

If a < b

If a ≤ b

If the relationship between a and b cannot be established

If a > b

If a ≥ b

Solution

Question 7

If a < b

If a ≤ b

If the relationship between a and b cannot be established

If a > b

If a ≥ b

Solution

Question 8

If a < b

If a ≤ b

If the relationship between a and b cannot be established

If a > b

If a ≥ b

Solution

Question 9

If a < b

If a ≤ b

If the relationship between a and b cannot be established

If a > b

If a ≥ b

Solution

Question 10

If x < y

If x > y

If x ≤ y

If x = y or the relationship between x and y cannot be established.

If x ≥ y

Solution

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Question Analysis

3x² + 5x - 2 = 0

3x² + 5x + 2 = 0

3x² - 5x + 2 = 0

3x² - 5x - 2 = 0