Equations and Inequalities Test

Result

Equations and Inequalities Test - 28

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Weekly Quiz Competition

Question 1
4 / -1

What is the sum of the squares of roots of x² – 3x + 1 = 0?

A
5

B
7

C
9

D
10

Solution
Question 2
4 / -1

A

B

C

D

Solution
Question 3
4 / -1

Product of real roots of the equation t²x² + |x| + 9 = 0

A
Is always positive

B
Is always negative

C
Does not exist

D
None of these

Solution
Question 4
4 / -1

If x be real, the latest value of x² – 6x + 10 is

A
1

B
2

C
3

D
10

Solution
Question 5
4 / -1

If sin α and cos α are the roots of the equation pχ² + qχ + r = 0, then

A
p² + q² - 2pr = 0

B
p² - q² + 2pr = 0

C
p² - q² - 2pr = 0

D
p² + q² + 2pr = 0

Solution
Question 6
4 / -1

In ∆ PQR, ∠R = π/2. If tan (P/2) and tan (Q/2) are the roots of aχ² + bχ + c = 0 , a ≠ 0, then

A
b = a + c

B
b = c

C
c = a + b

D
a = B + c

Solution
Question 7
4 / -1

Let α and β be real and z be a complex number. If z² + αz + β = 0 has two distinct roots on the line Re(z) = 1, then it is necessary that

A
β ϵ (-1, 0)

B
|β| = 1

C
β ϵ (1, ∞)

D
β ϵ (0 , 1)

Solution
Question 8
4 / -1

If (χ - 1)(χ² - 5χ + 7) < (χ - 1), then χ belongs to

A
(1,2) ∪ (3, ∞)

B
( -∞, 1) ∪ (2, 3)

C
(2, 3)

D
None of the above

Solution
Question 9
4 / -1

The greatest value of x + y + z for possible values of x, y, z such that x³ + y³ + z³ = 1 is

A
2^1/3

B
3^1/3

C
3^2/3

D
3^4/3

Solution
Question 10
4 / -1

The least value of a + b + c + d + e + f + g + h for possible values of a, b, c, d,e, f, g, and h satisfying the condition a^2/3 + b^2/3 + c^2/3 + d^2/3 + e^2/3 + f^2/3 + g^2/3 + h^2/3 = 4 is

A

B

C

D

Solution