MM
Mashaal Masha
Sep 29, 2022
Table of Contents
Choose the correct options for the following questions.
If $\alpha$ and $\beta$ are the roots of the equation $ax^{2}+bx+c=0$, then the equation with roots $\frac{1}{ \alpha}$ and $\frac{1}{ \beta}$ is
Verified
Difficulty: Easy
A:
$\frac{x^{2}}{ a}+\frac{x}{ b}+\frac{1}{ c}=0$
B:
$ay^{2}+by+c=0$
C:
$cy^{2}+by+a=0$
D:
$ax^{2}+bx+c=0$
If $n$ is any real number and $\omega^{n} =\omega^{2}$ where $\omega$ is cube root of unity then which of the following can be a possible value of n?
Verified
Difficulty: Easy
A:
$4$
B:
$-2$
C:
$6$
D:
$-1$
The equation which does not change by replacing $x$ with $\frac{1}{x}$ is known as
Verified
Difficulty: Easy
A:
Linear
B:
Proportional
C:
Quadratic
D:
None of these
$\omega^{-23} + \omega^{-28}$
Difficulty: Easy
A:
1
B:
$2\omega$
C:
0
D:
$\omega^{2}$
Product of cube roots of unity is
Verified
Difficulty: Easy
A:
0
B:
1
C:
$-1$
D:
$\omega$
If $x^{4}-3x^{2}-4=0$ then its roots are
Verified
Difficulty: Easy
A:
$2,-2,i$ and $-i$
B:
$1,-1,i$ and $-i$
C:
$i$
D:
None of these
Cube roots of unity are
Verified
Difficulty: Easy
A:
$1,\omega,\omega^{2}$
B:
$-1,1,\omega^{2}$
C:
$1,-1,\omega$
D:
None of these
Which of the following are the roots of the equation $x^{2}-3x-4=0$
Verified
Difficulty: Easy
A:
$1,4$
B:
$3,4$
C:
$-1,4$
D:
$-3,4$
What will be the value of $a$ in $x^{4}+x^{3}+ax+1$ if 1 is the root of the expression?
Verified
Difficulty: Easy
A:
0
B:
1
C:
$-2$
D:
$-3$
The sum of all the fourth roots of unity is
Verified
Difficulty: Easy
A:
0
B:
1
C:
$-1$
D:
$i$