- Content Type
CAT Previous Year Tests Previous Year CAT tests for training you for the D-Day. Time yourself, race against the competition and win it! Online CAT 2008 - Question Paper & Solutions Online CAT ...
If are complex numbers then is called a quadratic expression in x.
If are complex numbers then is called a quadratic equation in x.
If then is a root or solution of the quadratic equation
A quadratic equation can not have more than two roots or two solutions. The roots of are and its discrminent is .
The quadratic equation whose roots are and is
If a and c are of the same sign i.e, is +ve, then both the roots are of same sign.
If a and c are of opposite sign i.e, is -ve, then the roots are of opposite sign.
If both the roots are -ve, then a,b,c will have the same sign.
If both the roots are +ve then a, c will have the same sign different from the sign of b.
If a=c, then the roots are reciprocal to each other.
If a+b+c=0,then the roots are 1 and
If a+c=b, then the roots are -1 and
If the roots are in the ratio m:n then
If one root is p times the other root then
If one root is equal to the n th power of the other root
If one root is square of the other, then
If roots differ by unity, then
If and have the same roots then
The equations and where , have one common
and the common root is
If the equation has complex roots then and will have the same sign
If the equation has equal roots then and will have same sign
If the equation has real roots then
1. and will have opposite sign.
2. or and will have same sign.
If a > 0, then the minimum value of is (This value is attained at ).
If a < 0, then the maximum value of is (This value is attained at ).
If are the roots of then the equation whose roots are
Both the roots of equation are greater than a given number if
Both the roots of equation are smaller than a given number if
Exactly one root of lies between the numbers if
but f(p) and f(q) are not simultaneously zero.
Both the roots of equation lie between two given numbers if
The extreme values of are