Complex Numbers and Quadratic Equations Test 44

Result

Complex Numbers and Quadratic Equations Test 44

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Weekly Quiz Competition

Question 1
1 / -0

If $$a,b,c$$ are non-zero numbers and the equation $$ax^{2}+bx+c+i=0$$ has purely imaginary roots, then

A
$$a=bc$$

B
$$a=b^{2}c$$

C
$$a=\sqrt {bc}\ if\ b > 0$$

D
$$none\ of\ these$$

Solution
Question 2
1 / -0

The function of imaginary roots of the equation $$(x-1)(x-2)(3x+1)=32$$ is

A
$$0$$

B
$$1$$

C
$$2$$

D
$$4$$

Solution
Question 3
1 / -0

Let $$z,w$$ be complex numbers such that $$\vec {z}+i\vec {w}=$$ and $$zw=\pi$$ Then $$arg\ z$$ equals

A
$$\dfrac {\pi}{4}$$

B
$$\dfrac {5\pi}{4}$$

C
$$\dfrac {3\pi}{4}$$

D
$$\dfrac {\pi}{2}$$
Question 4
1 / -0

The equation $$x(x+2)(x^{2}-x)=-1$$, has

A
All roots imaginary

B
All roots negative

C
Two roots real and two roots imaginary

D
All roots real

Solution
Question 5
1 / -0

If $$\overline { \Delta } =\begin{vmatrix} -1 & 2-3i & 5+4i \\ 2+3i & 8 & 1-i \\ 5-4i & 1+i & 3 \end{vmatrix}$$ then $$\Delta =$$

A
Purely real

B
Purely imaginary

C
Complex

D
$$0$$

Solution
Question 6
1 / -0

Let $$z$$ be a complex number of maximum amplitude satisfying $$|z-3|=Re(z)$$, then $$|z-3|$$ is equal to

A
$$1$$

B
$$2$$

C
$$3/2$$

D
$$9$$
Question 7
1 / -0

Let $$A$$ and $$B$$ represent $$z_{1}$$ and $$z_{2}$$ in the Argand plane and $$z_{1},z_{2}$$ be the roots of the equation $$z^{2}+pz+q=0$$ where $$p,q$$ are complex numbers. If $$O$$ is the origin $$OA=OB$$ and $$\angle AOB=\alpha$$ then $$p^{2}=$$

A
$$2q\ \cos \left(\dfrac{\alpha}{2}\right)$$

B
$$4q\ \cos \left(\dfrac{\alpha}{2}\right)$$

C
$$4q\ \cos^{2} \left(\dfrac{\alpha}{2}\right)$$

D
$$4q^{2}\ \cos^{2} \left(\dfrac{\alpha}{2}\right)$$

Solution
Question 8
1 / -0

The number of imaginar roots of the equation $$(x-1)(x-2)(3x-2)(3x+1)=32$$ is

A
$$Zero$$

B
$$1$$

C
$$2$$

D
$$4$$

Solution
Question 9
1 / -0

If $$\mathrm{{z} _ { 1 }} = 10 + 6\mathrm{i} , \mathrm{{ z } _ { 2 }}= 4 + 6 \mathrm { i }$$ and $$\mathrm{ z}$$ is a complex number such that $$\operatorname { amp } \left( \dfrac { \mathrm { z } - \mathrm { z } _ { 1 } } { \mathrm { z } - \mathrm { z } _ { 2 } } \right) = \dfrac { \pi } { 4 }$$ , then the value of $$\left| \mathrm{z} - 7 - 9 \mathrm { i } \right|$$ is equal to

A
$$\sqrt { 2 }$$

B
$$2\sqrt { 2 }$$

C
$$3\sqrt { 2 }$$

D
$$2\sqrt { 3 }$$
Question 10
1 / -0

The number of distinct values of $$x$$ satisfying the equation $$\dfrac { x-2016 }{ 2015 } +\dfrac { x-2015 }{ 2016 } =\dfrac { 2015 }{ x-2016 } +\dfrac { 2016 }{ x-2015 }$$ is/are

A
$$0$$

B
$$1$$

C
$$2$$

D
$$3$$

Solution