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.