Recently Active Algebra Questions

if the equations x2 + 3x + 5 = 0 and ax2 + bx + c = 0 have a common root and a,b,c E N then find the minimum value of a + b + c. ...

factorize |x2(y - z) + y2(z - x) + z2(x - y)| Answer : |(x - y)(y - z)(z - x)| ...

In triangle ABC, we are given that 3sin{A}+4cos{B}=6 and 4sin{B}+3cos{A}=1 then find angle C. ...

if x3 + ax3 + 11x + 6 and x3 + bx2 + 14x + 8 have a common factor of the form x2 + px + q, then find (a + b). though i did it in 5 triels ... :P ... but a good prob (fr me atleast) so wanted to share. ...

Suppose n be a natural number such that |i+2i2 + 3i3+...+nin|=18√2. find n. ...

Here We have to find Min. of x^2+4 + (x-y)^2+4 + (y-14)^2+1 instead of taking point C(14,5) Why we can not take point C(14,3) explanation for that thing thanks *Image* ...

If any 7 numbers( not necessarily distinct ) are chosen from 2 to 12, prove that among those 7 numbers we can get three which form the sides of a triangle. ...

prove that the tens digit of every power integral power of 3 is an even number. like 3^5 = 243. here it is 4. ...

\hspace{-16}$Prove That\\\\ $\mathbf{(1)::\log_{2}{3}>\log_{3}{4}}$\\\\ $\mathbf{(2)::\log_{2}{3}>\log_{3}{11}}$\\\\ $\mathbf{(3)::\log_{3}{5}>\log_{2}{3}}$\\\\ without Using properties of Logarithms ...

Consider the cubic equation given by x3+ax2+bx+c = 0 , where a, b, c are real numbers. Which of the following is correct : A. If a2-2b < 0, then the equation has one real and two imaginary roots B. If a2-2b ≥ 0, then the ...

Q> Find the value of 'a' for which ax2 + (a - 3)x + 1 < 0 for at aleast one positive real x. ...

\hspace{-16}$Which one is Greater $\mathbf{2011^{2012}}$ OR $\mathbf{2012^{2011}}$ ...

Let tn be the no. of triangles with integral sides out of the side lengths {1,2,3,....n} . Then t20-t19 = ? ...

The condition that x4 + ax3 + bx2 + cx + d is a perfect square, is (A) c2 = ad (B) c2 = ad2 (C) c2 = a2d2 (D) c2 = a2d ???????????????? ...

find the factors of the no. 123456789 such that they have the minimum difference between them. ...

\hspace{-16}$If $\mathbf{x\;,y>0}$ and $\mathbf{xy+x+y=3}\;$.Then find Min. of \\\\\\ $\mathbf{P=\frac{x^2}{y+1}+\frac{y^2}{x+1}+\frac{xy}{x+y}}$ ...

\hspace{-16}$If $\mathbf{f(x)=x^3+x^2-4x+1}$ and If $\mathbf{\alpha}$ be a root of $\mathbf{f(x)=0}.\;$ Then Prove\\\\ that $\mathbf{\alpha^2+\alpha-3}$ is also root of $\mathbf{f(x)=0}$ ...

if the equation ax2 + bx + c = 0 does not have 2 distinct real roots and a + b > c, then prove that f(x) ≥ 0, for all x E R. ...

if x2 + ax + 3/x2 + x + a takes all real values for possible real values of x then prove that 4a3 + 39 < 0. ...

\hspace{-16}\mathbf{\displaystyle \sum_{k=0}^{1004} \frac{2008!}{k!\times k!\times (1004-k)!\times (1004-k)!}} ...

Find the values of 'a' for which the equation (x2 + x + 2)2 - (a - 3)(x2 + x + 2)(x2 + x + 1) + (a - 4)(x2 + x + 1)2 = 0 has atleast one real root. ...

How will you arrange all the digits from 1to9 forming different digits such that they form an A.P.? For example,consider 147,258,369. They form an A.P. with common difference 111,and all the digits from 1 to 9 are used . form ...

Someone please try to solve this problem. Two players A & B play a game of chess. Whoever wins first a total of two games wins. A's probability of winning,drawing or losing are p,q,r respectively. prove that the probability t ...

Can we solve this one? p^q - q^p=1927? the answer given was(2,11).......... ...

if |z1 + z2| > |z1 - z2| then prove that -pi/2 < arg(z1/z2) < pi/2 ...

*Image* help me please...!! ...

1. find the number of complex numbers satisfying |z| = z + 1 + 2i. 2. If z + √2 |z + 1| + i = 0 and z = x + iy then x = ? 3. if p2 + q2 = 1, p,q E R, then 1 + p + iq/1 + p - iq is equal to (A) p + qi (B) p - qi (C) q + pi ( ...

\dpi{120} \hspace{-16}\frac{\binom{2010}{0}}{1.1}+\frac{\binom{2010}{2}}{3.4}+\frac{\binom{2010}{4}}{5.4^2}+\frac{\binom{2010}{6}}{7.4^3}+..................+\frac{\binom{2010}{2010}}{2011.4^{1005}}=\\\\\\ $Where $\binom{n}{r} ...

*Image* If z1 and z2 are two complex numbers in the argand plane shown..!! then what does (z2 - z1) represent? ...

if iz3 - z2 - z + i = 0, then show that |z| = 1 The solution given in my book is something like this... (z - i)(iz2 - 1) = 0 so, z = i => |z| = 1 (i got it till here) but, (iz2 - 1) = 0 then how can |z| = 1 ?? (plese help ...