Quant by Arun Sharma

[setu_sin]

Guys is there a method to solve polynomial equations ...the way we factorize for quadratic equations... like for an equation :

x^2 + 5x +6 ... we factorize 6 and get 2 and 3 ,thus expanding the eqn as
x^2 + 3x +2x +6....

how would we do it for say ... x^3 -7x^2 +21x -27 =0?

[shivam_01]

Originally Posted by setu_sin

Guys is there a method to solve polynomial equations ...the way we factorize for quadratic equations... like for an equation :

x^2 + 5x +6 ... we factorize 6 and get 2 and 3 ,thus expanding the eqn as
x^2 + 3x +2x +6....

how would we do it for say ... x^3 -7x^2 +21x -27 =0?

By either hit or trial u put the values and check the remainder for x=-1,1,-2,2.. so on
when the remainder is 0 then divide the equation by that value

else u can take the roots as a,b,c
where
a+b+c=-coefficient of x^2/coefficient of X^3

ab+bc+ca = coefficient of x/coefficient of X^3

abc = constant term /coefficient of X^3

use these to solve for a,b,c

[varunj1984]

hi here r some questions..though u might say its basic..but still i was unable to do it..plz explain concepts...while solving,,,.Is there some tutorials or concepts section where I can find such concepts...to understand..

1.value of the expression (x^2-x+1)/(x-1) cannot lie between
a) 1,3 b) -1,-3 c) 1,-3 d) -1,3

2.
Sum of the real roots of the equation x^2+5|x|+6 =0 is

3.If the expression ax^2+bx+c is equal to 4 when x = 0 leaves a remainder 4 when divided by x+1 and a remainder 6 when divided by x+2,than the values of a,b and c are ?

4.
Log(9-2^x)base 2 = 10^log(3-x) solve for x

[billibite]

Hi I am total noob with CAT and Quant prep.
So my doubt comes from the first chapter i.e Numbers.
Can anyone explain to me how the remainder of 21^875 / 17 can be found? Using remainder theorom only.
Or in general any division where the Numerator is raised to a large power.

[shashank3012]

@billibite
[21^875]/17
[(17+4)^875]/17
[4^875]/17
[16^873]/17
[(17-1)^873]/17
[-1^873]/17
So,-1.Hence,answer should be 16.Its better to apply remainder theorem for these sums.

[vineet.nitd]

Originally Posted by billibite

Hi I am total noob with CAT and Quant prep.
So my doubt comes from the first chapter i.e Numbers.
Can anyone explain to me how the remainder of 21^875 / 17 can be found? Using remainder theorom only.
Or in general any division where the Numerator is raised to a large power.

Hi dude. Would ask you to go through the questions discussed on Number System thread. You will get to learn useful tools to crack these number related problems.

For your question 21^875 / 17=>4^875 / 17

Also, 4^16k = 17x+1. Hence 4^875 / 17 = 4^11/17=4*(-1)^5= 13
So, remainder is 13.

[priyatip]

Can sum1 help me 2 solve da qn: The sum of series represented as:
1/1*5+ 1/5*9+ 1/9*13 +--- --+1/221*225 is:
options:
a)28/225 b)56/221
c)56/225 d)none of these
thanx in advance

[shivam_01]

Originally Posted by priyatip

Can sum1 help me 2 solve da qn: The sum of series represented as:
1/1*5+ 1/5*9+ 1/9*13 +--- --+1/221*225 is:
options:
a)28/225 b)56/221
c)56/225 d)none of these
thanx in advance

welcome to PG priya

my take::
see u can write the general term as 1/(n*n+4) now in this case
1/4(1/n-1/n+4) now applying values we get
1/4(1-1/5+1/5-1/9.......1/224-1/225)
all the terms will cancel out except
1/4(1-1/225) so the answer is 56/225

am i correct

[shivam_01]

Originally Posted by billibite

Hi I am total noob with CAT and Quant prep.
So my doubt comes from the first chapter i.e Numbers.
Can anyone explain to me how the remainder of 21^875 / 17 can be found? Using remainder theorom only.
Or in general any division where the Numerator is raised to a large power.

answer to this is 13
21^875 mod 17
4^875 mod 17
(4^2)*odd *4
so (17-1)^odd*4 mod 17 answer is 16*4 mod 17 = 13
So, remainder is 13.

@ shashank check the bold part

@billibite
[21^875]/17
[(17+4)^875]/17
[4^875]/17
[16^873]/17
[(17-1)^873]/17
[-1^873]/17
So,-1.Hence,answer should be 16.Its better to apply remainder theorem for these sums.

[shivam_01]

my take::
answers

1.value of the expression (x^2-x+1)/(x-1) cannot lie between
a) 1,3 b) -1,-3 c) 1,-3 d) -1,3

max and min value of this expression is -1 and 3 hence option 2 is out of the question

2.
Sum of the real roots of the equation x^2+5|x|+6 =0 is

roots are -3,-2,3,2 sum is 0

3.If the expression ax^2+bx+c is equal to 4 when x = 0 leaves a remainder 4 when divided by x+1 and a remainder 6 when divided by x+2,than the values of a,b and c are ?

a=1,b=1,c=4

4.
Log(9-2^x)base 2 = 10^log(3-x) solve for x

what is the base for other log