Recent questions tagged ch5

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

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$a$ 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

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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

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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

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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

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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

$a,b,c$ 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.The common root is :

asked Apr 15, 2014 by sreemathi.v

1 answer

The set of values of 'a' for which roots of equation $3x^2+2x+(a-1)a=0$ are of opposite sign

asked Apr 15, 2014 by sreemathi.v

1 answer

$\sin \theta$ and $\cos\theta$ are roots of equation $ax^2+bx+c=0$ then,

asked Apr 15, 2014 by sreemathi.v

1 answer

The value of P for which the sum of squares of roots of equation $x^2-(p-2)x-(p+1)=0$ attains the least value is :

asked Apr 15, 2014 by sreemathi.v

1 answer

Roots of equation $x^2+px-q=0$ are $\tan 30^{\large\circ}$ and $\tan 15^{\large\circ}$,then value of $2-q-p$ is :

asked Apr 15, 2014 by sreemathi.v

1 answer

If one root of $(a^2-5a+3)x^2+(3a-1)x+2=0$ is double the other,then the value of a is :

asked Apr 15, 2014 by sreemathi.v

1 answer

If one root of the equation $8x^2-6x-k-3=0$ is square of other,then value of $k$ is

asked Apr 14, 2014 by sreemathi.v

1 answer

Values of $\lambda$ for which $(\lambda^2-5\lambda+6)x^2+(\lambda-3\lambda+2)x+\lambda^2-4=0$ is an identity in x is:

asked Apr 14, 2014 by sreemathi.v

1 answer

$\alpha^2=5\alpha-3,\beta^2=5\beta-3\quad(\alpha\neq \beta)$,then the equation whose roots are $\large\frac{\alpha}{\beta}$ and $\large\frac{\beta}{\alpha}$ is :

asked Apr 14, 2014 by sreemathi.v

1 answer

The equation whose roots A.M=9 and G.M=4 is

asked Apr 14, 2014 by sreemathi.v

1 answer

Roots of equation $(b-c)x^2+(c-a)x+(a-b)=0$ are

asked Apr 14, 2014 by sreemathi.v

1 answer

Number of roots of equation $x-\large\frac{2}{x-1}$$=1-\large\frac{2}{x-1}$ is

asked Apr 14, 2014 by sreemathi.v

1 answer

If $\alpha,\beta$ are the roots of $ax^2+bx+c=0$ then equation whose roots are $2+\alpha,2+\beta$ are

asked Apr 14, 2014 by sreemathi.v

1 answer

Roots of the equation $12x^2+mx+5=0$ are in the ratio $3 : 2$,then $m$ equals

asked Apr 14, 2014 by sreemathi.v

1 answer

If $x$ is real,$\large\frac{x^2+3yx-71}{x^2+2x-7}$ cannot lie between

asked Apr 14, 2014 by sreemathi.v

1 answer

Range of $y=\large\frac{x+2}{2x^2+3x+6}$ if $x$ is real is :

asked Apr 14, 2014 by sreemathi.v

1 answer

The range of $y=\large\frac{x^2-x+1}{x^2+x+1}$ if $x$ is real

asked Apr 14, 2014 by sreemathi.v

1 answer

If $ax^2-bx+5=0$ does not have two distinct real roots,then minimum value of $5a+b$ is

asked Apr 14, 2014 by sreemathi.v

1 answer

$\alpha,\beta$ are roots of equation $ax^2+bx+c=0$.Equation whose roots are $\large\frac{1-\alpha}{\alpha}$ and $\large\frac{1-\beta}{\beta}$ are

asked Apr 14, 2014 by sreemathi.v

1 answer

Find the real numbers x and y if $\;(x-iy)(3+5i)\;$ is the conjugate of $\;-6-24i$

asked Apr 14, 2014 by yamini.v

1 answer

Find the modulus and argument of the complex number $\;\large\frac{1+2i}{1-3i}$

asked Apr 14, 2014 by yamini.v

1 answer

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