maths
posted by sapna on .
If ax^2 + bx + c = 0 If a,b,c E R. Find the condition that this equation would have atleast one root in [0,2].

a x ^ 2 + b x + c = a ( x  x1 ) ( x  x2 )
In this case :
a x ^ 2 + b x + c = a ( x  0 ) ( x  2 ) = a x ( x  2 ) = a ( x ^ 2  2 x ) 
plse explain me again, i didn't get it..

plsee ..i need urgent

If x1 and x2 are two roots of equation
a x ^2 + b x + c =0
then
a x ^ 2 + b x + c = a ( x  x1 ) ( x x2 ) 
a
is leading coefficient 
That is true for any value of a
example:
3 ( x ^ 2  2 x ) = 0
has roots 0 and 2
7 ( x ^ 2  2 x ) = 0
has roots 0 and 2
39 ( x ^ 2  2 x ) = 0
has roots 0 and 2
etc. 
Thank You so much..