Hii all....
here are some of the time saving points for ur COMPETITIVE EXAMS , hope u enjoy these....
1) In qs like...
(5 + 2root 6)x^2-3 + (5 - 2root 6)x^2 - 3 = 10.....
i mean powers same , n coeff of root wali term is -ive of the other ,
just take the power = 1 n -1 resp.
like here
x2-3 = 1 , n x2 - 3 = -1
now solve , u get the answer...
CONDITION -----> the power must must must be a polynomial of degree 2 or more.....( 1 nai)
and dont use this in CBSE......teacher will give u a Big ZERO :D
2)whenever , roots of polynomial are distinct ,
f(0)*f(1) < 0
this is knwn as DISCART's method....
like in qs...
x3 - 3x + a = 0 has distinct roots in (0,1) , then find "a"...
well we cant find the exact value , but we can find the range....
a(a-2) < 0,
so 0 < a < 2....
3) please remember this property ,
alog (base a) N = N......it may help u in quad =ns many times....
4) some common points in matrices....ratta maaro ya kuch bi.....bt learn them plzz....
a)If A is an orthogonal matrix , then A-1 equals At (t - transpose)
b)If A,B are 2 square matrices , such that A.B = A & B.A = B , then A & B both are independent or idempotent matrix...
c) The inverse of a symmetric matrix is a symm. matrix , that of a diagonal matrix is a diagonal matrix
d)If A,B are symm matrix of same order , then AB - BA is a skew symm matrix....
e)Trace of a matrix = sum of elements of primary diagonal...
f)Trace of a skew symm matrix is zero
g)rank of a null matrix doesnt exist....
h)If A is an invertible matrix , then
|A-1| = 1 / |A|
mmm....well these are some points.....maybe given in some books , maynot be given....
but we dun see them frm book i knw.....so posted them here....
but i dun have copied it frm a single book , these are all my notes....may be collected frm different-2 books.....so wrote here collectively
hope it helps.....
ALL THE BEST :)
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