Equations and Inequalities Test

Result

Equations and Inequalities Test - 5

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
4 / -1

If α and β are the roots of χ² - 2χ + 4 = 0, then thevalue of α⁶ + β⁶ is

A
32

B
64

C
128

D
256

Solution
Question 2
4 / -1

If α ,β and γ are the roots of χ³ + 4χ + 1 = 0, then the equation, whose roots are

A
χ³ - 4χ - 1 = 0

B
χ³ - 4χ + 1 = 0

C
χ³ + 4χ - 1 = 0

D
χ³ + 4χ + 1 = 0

Solution
Question 3
4 / -1

The number of real solutions of the equation | x |² – 3 | x | + 2 = 0 is

A
4

B
1

C
3

D
2

Solution
Question 4
4 / -1

If α ,β and γ are such that α + β + γ = 2, α² + β² + γ² = 6, α³ + β³ + γ³ = 8 then α⁴ + β⁴ + γ⁴ is equal to

A
7

B
12

C
18

D
36

Solution
Question 5
4 / -1

Let the two numbers have arithmetic mean 9 and geometric mean 4. Then, these numbers are the roots of the quadratic equation

A
χ² - 18χ - 16 = 0

B
χ² - 18χ +16 = 0

C
χ² + 18χ - 16 = 0

D
χ² + 18χ + 16 = 0

Solution
Question 6
4 / -1

If α and β are the roots of the equations χ² - (1 + n² )χ+ 1/2(1 + n² + n⁴) = 0, then α² + β² is equal to

A
n²

B
- n²

C
n⁴

D
- n⁴

Solution
Question 7
4 / -1

If α and β are the roots of χ² - 2χ cos ∅ + 1 = 0, then the equation, whose roots are αⁿ + βⁿ

A
χ² - 2 χcos n∅ - 1 = 0

B
χ² - 2 χcos n∅ + 1 = 0

C
χ² - 2 χsin n∅ + 1 = 0

D
χ² + 2 χsin n∅ - 1 = 0

Solution
Question 8
4 / -1

If α, β and γ are the roots of the equation χ³ - 8 χ + 8 = 0, then ∑a² and ∑ 1/αβ are respectively

A
0 and - 16

B
16 and 18

C
- 16 and 0

D
16 and and 0

Solution
Question 9
4 / -1

If α and β are the roots of the equation aχ² + bχ + c = 0, αβ = 3, and a, b, c are in AP, then α + β is equal to

A
- 4

B
1

C
4

D
- 2

Solution
Question 10
4 / -1

If α and β are the roots of the equation χ² + aχ + b = 0, then

A

B

C

D

Solution