Equations and Inequalities Test

Result

Equations and Inequalities Test - 22

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Weekly Quiz Competition

Question 1
4 / -1

If the roots of the equation bχ² + cχ + a = 0 is imaginary, then for all real values of χ, the expression 3b² χ² + 6bcχ + 2c² is

A
greater than 4ab

B
less than 4ab

C
greater than – 4ab

D
less than – 4ab

Solution
Question 2
4 / -1

If a, b and c are in GP, then the equation aχ² + 2bχ + c = 0 and dχ² + 2eχ + f = 0 have a common root, if d/a, e/b and f/c are in

A
AP

B
HP

C
GP

D
None of these

Solution
Question 3
4 / -1

If ax² + bχ + c = 0 and 2χ² + 3χ + 4 = 0 have a common root, where a, b, c ∈ N (set of natural numbers), then the least value of a + b + c is

A
13

B
11

C
7

D
9

Solution
Question 4
4 / -1

A
a = -1, b =1

B
a = 1, b = - 1

C
a = 5, b = 9

D
a = 9, b = 5

Solution
Question 5
4 / -1

The quadratic equations χ² - 6χ + a = 0 χ² - cχ + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then, the common root is

A
2

B
1

C
4

D
3

Solution
Question 6
4 / -1

Let a, b and c be real. If aχ² + bχ + c = 0 has two real roots α and β where α < - 1 and β > 1 , then

A
< 0

B
> 0

C
≤ 0

D
None of these

Solution
Question 7
4 / -1

All the values of m for which both roots of the equation χ² - 2mχ + m² - 1 = 0 are greater than - 2 but less than 4 lie in the interval

A
m > 3

B
- 1 < m < 3

C
1 < m < 4

D
- 2 < m < 0

Solution
Question 8
4 / -1

The values of k, for which the equations χ² - kχ - 21 = 0 and χ² - 3kχ + 35 = 0 will have a common roots, is

A
K = ± 4

B
K = ± 1

C
K = ± 3

D
K = 0

Solution
Question 9
4 / -1

If the both the root of the quadratic equation χ² - 2kχ + k² + k - 5 = 0 are less than 5, then k lies in the interval

A
(4, 5)

B
(- ∞, 4)

C
(6, ∞)

D
(5, 6)

Solution
Question 10
4 / -1

If χ is real, then the value of

A

B

C

D
None of these

Solution