Question

determine the condition for the roots of the equation ax2+bx+c=0 to differ by 2

Answer 1

when the
D<0
in this condition the roots can differ by 2

Answer 2

The condition for the roots of the equation ax2+bx+c=0 to differ by 2 is 4*a^2 = b^2 - 4*c*a .

• We know that ,

     ( e - f ) ^ 2 = ( e + f ) ^ 2 - 4*e*f

• Let e and f be the two roots of the given equation .  

• Sum of the roots , ( e + f ) =   ( -b / a)

• Product of the roots , ( e*f ) = ( c / a )

• Then,

       ( 2 ) ^ 2 = ( -b / a ) ^ 2 - 4*( c / a)

        4*a^2 = b^2 - 4*c*a