Recently Active Algebra Questions

1. All the three roots of equation x3 –- 3x +1 = 0 lie on the interval (A) [–2, 0] (B) [–1, 1] (C) [–2, 2] (D) [–1, 2] 2. If ax2 + bx + c, a, b, c belog to R has no real zeros and if a + b + c < 0 then (A) c > 0 (B ...

Q. If the roots of the equation ax2+bx+c=0 , are of the form α/α-1 and α+1/α , then the value of (a+b+c)2 is? [ans - b2-4ac] I got the answer by putting any value of alpha but how to solve it in subjective form ...

$\textbf{The equation $\mathbf{x^4+ax^3+bx^2+ax+c=0,a,b,c\in\mathbb{R}$} }$\\\\ $\textbf{has all real roots . Then Prove that $\mathbf{\sqrt{|1-b+c|}\geq 1+\sqrt{|c|}}$} ...

$\textbf{Solve for $\mathbf{x}$: }$\\\\ \mathbf{\sqrt{12-\frac{12}{x^2}}+\sqrt{x^2-\frac{12}{x^2}}=x^2}$ ...

\textbf{Solve System of Equations: }$\\\\\left\{\begin{matrix} \mathbf{\sqrt{x^2+y^2}=z+1} \\\\ \mathbf{\sqrt{y^2+z^2}=x+1} \\\\ \mathbf{\sqrt{z^2+x^2}=y+1} \end{matrix}\right;\mathbf{x.y,z\in\mathbb{R}} . ...

Simplify \left({\sqrt{75}-\sqrt{12}}\right)^{-2/3} ...

$\textbf{If $\mathbf{z_{1}}$ and $\mathbf{z_{2}}$ are two distinct Complex no. such that $\mathbf{|z_{1}|=|z_{2}|}$\\\\ and $\mathbf{Re(z_{1})>0}$ and $\mathbf{Im(z_{2})<0}$.Then find value of $\mathbf{\displaystyle \fr ...

$If $x,y,z$ are real no. such that $\left\{\begin{array}{c} x+y+z=2\\ x^2+y^2+z^2=16\\ xyz=1\end{array}\right.$ .\\\\\\ Then Calculate value of $\displaystyle \frac{1}{xy+2z}+\frac{1}{yz+2x}+\frac{1}{zx+2y}=$ ...

$\textbf{Calculate value of $\mathbf{x}$ in }$\\\\ \mathbf{\left[\frac{x}{1!}\right]+\left[\frac{x}{2!}\right]+\left[\frac{x}{3!}\right]+.................+\left[\frac{x}{2007!}\right] = 1005}$\\\\ \textbf{Where $\mathbf{\left ...

[log {(log a)/(log b)} x (log b) / (log a)] / log {(log b)/(log a)} ...

summation r=1 to r=101 of, (r)*(101-r)c50 ...

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If in an AP,the sum of m terms is equal to sum of next n terms as well as sum of next p terms,then prove: (m+n){(1/m) -(1/p)}=(m+p){(1/m)-(1/n)} My attempt: from given information we can say that 2m{2a+(m-1)d}=(m+n){2a+(m+n-1 ...

There are n children on a merry-go-round. They' decide to change places so that somebody else is in front of each one. In how many ways can they achieve this? ...

what is its significance?how is it useful? ...

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Can anyone and every one post some JEE level problems on BINOMIAL theorom. Thnks! ...

doubt-1: *Image* doubt-2: *Image* in this second doubt i can't understand how we came up with the condition to be satisfied for one root to be sqaure of other? ...

Do we need to memorize all the results of the expansions...mainly in the topic binomial coefficients...??? Which book is better for MATH arihant or TMH??? ...

Suppose we construct a plane such that it only contains points whose ordinates as well the abscissae are integers . Each point of this plane is labeled by a positive integer . Each of these numbers is - 1 > The arithmetic ...

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*Image* i have read that irrational roots must be conjugates and not a multiple in this case..or have i completely misunderstood the question? ...

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If a,b,c,d and p are Real. (a2+b2+c2)p2-2(ab+bc+cd)p+(b2+c2+d2)≤0 a,b,c,d are in ___? ...

Let Sn denote sum of first n terms of an AP.If S2n = 3 Sn then ratio S3n:Sn=? had been trying it for whole day today but unable to solve it so finally sending it here! ...

problem-1: a, b be real numbers such that 0 ≤ a ≤ b ≤ 1. prove: 0 ≤(b − a)/(1 − ab) ≤ 1, ...

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Find sum of first hundred terms appearing in BOTH 17,21,25......... and 16,21,26............ ...

targetiit is a website where no experts like to come ...

http://www.targetiit.com/iit-jee-forum/posts/progressions-solution-needed-19365.html ...