Recent questions in Complex Numbers and Quadratic Equations

Find the conjugate of $\;\large\frac{(3-2i)(2+3i)}{(1+2i)(2-i)}$

asked Apr 16, 2014 by yamini.v

1 answer

Solve $\; \sqrt{5} x^{2} + x + \sqrt{5}=0$

asked Apr 16, 2014 by yamini.v

1 answer

Solve $\;x^{2} + x + 1=0$

asked Apr 16, 2014 by yamini.v

1 answer

Solve $\;x^{2}+2 =0 \;$

asked Apr 16, 2014 by yamini.v

1 answer

Convert the complex number $\;\large\frac{-16}{1+i \sqrt{3}} \;$ into polar form

asked Apr 16, 2014 by yamini.v

1 answer

Represents the complex number $\;z=1+ \sqrt{3} i \;$ in the polar form

asked Apr 16, 2014 by yamini.v

1 answer

Express the following in the form $\;a+ib : i^{-35}$

asked Apr 16, 2014 by yamini.v

1 answer

Express the following in the form $\;a+ib : \large\frac{5 + \sqrt{2} i }{1 - \sqrt{2} i}$

asked Apr 16, 2014 by yamini.v

1 answer

Find the multiplicative inverse of $\;2 - 3 i$

asked Apr 16, 2014 by yamini.v

1 answer

Express $\;(- \sqrt{3} + \sqrt{-2})(2 \sqrt{3} - i)\;$ in the form $\;a+ib$

asked Apr 16, 2014 by yamini.v

1 answer

Express $\;(5-3i)^{3}\;$ in the form of $\;a+ib$

asked Apr 16, 2014 by yamini.v

1 answer

Express the following in the form of $\;a+bi : (-i) \; (2i)\;(-\large\frac{1}{8}i)^{3}$

asked Apr 16, 2014 by yamini.v

1 answer

Express the following in the form of $\;a+bi : (-5i) \; (\large\frac{1}{8}i)$

asked Apr 16, 2014 by yamini.v

1 answer

If $\;4x+i(3x-y)=3+i (-6)\;$ where x and y are real numbers , then find the values of x and y

asked Apr 16, 2014 by yamini.v

1 answer

If the equation $ax^2+bx+c=0$ $(a > 0)$ has roots $\alpha$ and $\beta$ such that $\alpha < -2$ and $\beta > 2$ then,

asked Apr 16, 2014 by sreemathi.v

1 answer

Sum of rational roots of $x^5=\large\frac{133x-78}{133-78x}$ is

asked Apr 16, 2014 by sreemathi.v

1 answer

Sum of all integral roots of $(\log_5x)^2+\log_{5x}(\large\frac{5}{x})$ $=1$ is

asked Apr 16, 2014 by sreemathi.v

1 answer

Given $x+y+z=4$ and $x^2+y^2+z^2=6$ .The range of z is $[\large\frac{2}{3}$ $,k]$ .The value of k is

asked Apr 16, 2014 by sreemathi.v

1 answer

Given,for three distinct real numbers a,b,c $\in R,a(a^2+p)=b(b^2+p)=c(c^2+p)$ .The value of $a+b+c$ is

asked Apr 16, 2014 by sreemathi.v

1 answer

The least integral value of m for which every solution of inequality $1 \leq x\leq 2$ is solution of the inequality $x^2-mx+1 < 0$

asked Apr 16, 2014 by sreemathi.v

1 answer

Number of polynomials p(x) with integral coefficients satisfying the condition p(1)=2 and p(3)=1 are

asked Apr 16, 2014 by sreemathi.v

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The real value of a for which the roots $x_1,x_2,x_3$ of $x^3-6x^2+ax-a=0$ satisfy $(x_1-3)^3+(x_2-3)^3+(x_3-3)^3=0$ is

asked Apr 16, 2014 by sreemathi.v

1 answer

Number of solution of $2\cos^2(\large\frac{x}{2})=$ $(0.2)^x+(0.2)^{-x}$ are

asked Apr 16, 2014 by sreemathi.v

1 answer

$a$ and $b$ are two integers such that $10a+b=5$ and $p(x)=x^2+ax+b$ .The value of n such that $p(10)p(11)=p(n)$

asked Apr 16, 2014 by sreemathi.v

1 answer

Given $a,b,c > 0,a^2=bc$ and $a+b+c=abc$ ,the least possible value of $a^2$ is

asked Apr 16, 2014 by sreemathi.v

1 answer

If $x_1$ and $x_2$ are roots of the equation $x^2+x+c=0\quad c\neq 0$ and $\large\frac{x_1^3}{2+x_2}+\frac{x_2^3}{2+x_1}=\frac{-1}{2}$ the value of -4c is

asked Apr 16, 2014 by sreemathi.v

1 answer

Let $a,b$ be two distinct roots of $x^4+x^3-1=0$ and $p(x)=x^6+x^4+x^3-x^2-1$

asked Apr 16, 2014 by sreemathi.v

1 answer

Let $f(x)=x^3+3x^2+6x+2009$ and $g(x)=\large\frac{1}{x-f(1)}+\frac{2}{x-f(2)}+\frac{3}{x-f(3)}$ .The no of real solutions of $g(x)$ =0 is :

asked Apr 16, 2014 by sreemathi.v

1 answer

If $\;(\large\frac{1+i}{1-i})^{m}=1\;$ then find the least positive integral value of m

asked Apr 15, 2014 by yamini.v

1 answer

Find the number of non - zero integral solutions of the equation $\;|1-i|^{x}=2^{x}$

asked Apr 15, 2014 by yamini.v

1 answer

If $\cot\theta,cosec \theta$ are the roots of the equation $ax^2+bx+c=0$ and $\Delta=b^2-4ac$ ,then $a^4$ equals

asked Apr 15, 2014 by sreemathi.v

1 answer

If $\;\alpha\;$ and $\;\beta\;$ are different complex numbers with $\;|\beta=1|\;$ , then find $\;|\large\frac{\beta-\alpha}{1-\overline{\alpha} \beta}|$

asked Apr 15, 2014 by yamini.v

1 answer

If $\;(x+iy)^{3}=u+iv\;$ , then show that $\; \large\frac{u}{x} + \large\frac{v}{y} = 4(x^{2}-y^{2})$

asked Apr 15, 2014 by yamini.v

1 answer

Find the modulus of $\;\large\frac{1+i}{1-i} - \large\frac{1-i}{1+i}$

asked Apr 15, 2014 by yamini.v

1 answer

The set of values of b for which $2\log_{1/36}(bx+28)=-\log_6(12-4x-x^2)$ has exactky one solution is

asked Apr 15, 2014 by sreemathi.v

1 answer

Number of irrational roots of the equation $(x^2-3x+1)(x^2+3x+2)(x^2-9x+20)=-30$ are

asked Apr 15, 2014 by sreemathi.v

1 answer

The number of irrational solutions of $\sqrt{x^2+\sqrt{x^2+11}}+\sqrt{x^2-\sqrt{x^2+11}}=4$ are

asked Apr 15, 2014 by sreemathi.v

1 answer

The set of all values of 'a' for which the roots of the equation $(1+a)x^2-3ax+4a=0$ exceeds 1

asked Apr 15, 2014 by sreemathi.v

1 answer

Given $\alpha,\beta,\gamma$ such that $\alpha+\beta+\gamma=2,\alpha^2+\beta^2+\gamma^2=6,\alpha^3+\beta^3+\gamma^3=8$ ,then the value of $\alpha^4+\beta^4+\gamma^4$ is equal to

asked Apr 15, 2014 by sreemathi.v

1 answer

Let roots of equation $x^2-ax+b$ be $\alpha,\beta$ .Given $A_n=\alpha^n+\beta^n$ then, $A_{n+1}-aA_n+bA_{n-1}$ is equal to

asked Apr 15, 2014 by sreemathi.v

1 answer

If $x$ is real,then maximum value of $y=2(a-x)(x+\sqrt{x^2+b^2})$ is

asked Apr 15, 2014 by sreemathi.v

1 answer

Value of 'a' for which $x^2-(a+2)x+2a$ is perfect square is :

asked Apr 15, 2014 by sreemathi.v

1 answer

Given, $a(p+q)^2+2bpq+c=0$ and $a(p+r)^2+2bpr+c=0$ .Then the value of qr is

asked Apr 15, 2014 by sreemathi.v

1 answer

$\alpha,\beta$ are roots of $ax^2+bx+c=0$ .The value of $(a\alpha+b)^{-2}+(a\beta+b)^{-2}$ is

asked Apr 15, 2014 by sreemathi.v

1 answer

$a,b\in R$ ,roots of $x^2+ax+b=0$ are $\alpha,\beta$ and roots of $x^2+bx+a=0$ are $\alpha+k,\beta+k$ where $k\neq 0$ . $\alpha,\beta,k$ are real,a & b are positive,then

asked Apr 15, 2014 by sreemathi.v

1 answer

$a,b\in R$ ,roots of $x^2+ax+b=0$ are $\alpha,\beta$ and roots of $x^2+bx+a=0$ are $\alpha+k,\beta+k$ where $k\neq 0$ .If $ab=\lambda$ ,then interval for $\lambda$ is

asked Apr 15, 2014 by sreemathi.v

1 answer

$a,b\in R$ ,roots of $x^2+ax+b=0$ are $\alpha,\beta$ and roots of $x^2+bx+a=0$ are $\alpha+k,\beta+k$ where $k\neq 0$ .Which of the following is true?

asked Apr 15, 2014 by sreemathi.v

1 answer

$a,b,c$ are natural no and equations $x^2-5x+a=0,x^2-6x+b=0,x^2-8x+c=0$ have exactly one root in common and common root is also a natural no. $b+c$ is maximum when common root is :

asked Apr 15, 2014 by sreemathi.v

1 answer

$a,b,c$ are natural no and equations $x^2-5x+a=0,x^2-6x+b=0,x^2-8x+c=0$ have exactly one root in common and common root is also a natural no. $(a+b+c)$ is minimum when common root is :

asked Apr 15, 2014 by sreemathi.v

1 answer

$a,b,c$ are natural no and equations $x^2-5x+a=0,x^2-6x+b=0,x^2-8x+c=0$ have exactly one root in common and common root is also a natural no.(a+b+c) is maximum when common root is :

asked Apr 15, 2014 by sreemathi.v

1 answer

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