Equations and Inequalities Test

Result

Equations and Inequalities Test - 8

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Weekly Quiz Competition

Question 1
4 / -1

If a + b + c = 0, then the roots of the equation 4aχ² + 3bχ + 2c = 0 are

A
equal

B
imaginary

C
real

D
None of these

Solution
Question 2
4 / -1

The roots of equation χ³ - 6χ + 9 = 0 is

A
-6

B
-9

C
6

D
-3

Solution
Question 3
4 / -1

The equation χ² - 3|χ| + 2 = 0 has

A
no real root

B
one real root

C
two real roots

D
four real roots

Solution
Question 4
4 / -1

A value of K for which the quadratic equation χ² - 2χ (1 + 3K) + 7(2K + 3) = 0 has equal roots, is

A
1

B
2

C
3

D
4

Solution
Question 5
4 / -1

If p, q, r are any real numbers, then

A
max (p, q) < max (p, q, r)

B

C
max (p, q) < min (p, q, r)

D
none of these

Solution
Question 6
4 / -1

If p, q and r real and p q, then the roots of the equation (p - q)χ² + 5(p + q)χ - 2(p - q) = r are

A
real and equal

B
unequal and rational

C
unequal and irrational

D
nothing can be said -

Solution
Question 7
4 / -1

The number of real roots of the equation

A
0

B
2

C
4

D
6

Solution
Question 8
4 / -1

If (1 - p) is a root of quadratic equation χ² + pχ + (1 - p) = 0, then its roots are

A
0, 1

B
- 1, 1

C
0, - 1

D
- 1, 2

Solution
Question 9
4 / -1

If e^{cos χ} - e^{-cos χ} = 4, then the value of cos χ is

A
log(2 + √5)

B
- log(2 + √5)

C
log( - 2 + √5)

D
None of the above

Solution
Question 10
4 / -1

The number of real solutions of the equation

A
0

B
1

C
2

D
None of these

Solution