If R is such that the sum of the cubes of the roots of the equation, x^2+(2- ) x+(10- )=0 is minimum, then the magnitude of the difference of the roots of this equation is

Step-by-step solution

Let, the roots of the equation, x^2+(2- ) x+(10- )=0 are and . Also roots of the given equation are -2 4-4 + ^2-40+4 2 = -2 ^2-36 2 The magnitude of the difference of the roots is | ^2-36 | So, ^3+ ^3= ( -2)^3 4 + 3( -2) ( ^2-36 ) 4 aligned = ( -2) (4 ^2-4 -104 ) 4 =&( -2) ( ^2- -26 )=f( ) aligned As f( ) attains its minimum value at =4 . Therefore, the magintude of the difference of the