Find the absolute value of the difference of the real roots of the equation `x^2-2^(2010)x+|x-2^(2009)|+2(2^(4017)-1)=0`

Let a be a non-zero real number and alpha, beta be the roots of the equation ax^(2) + 5x + 2 = 0 . Then the absolute value of the difference of the roots of the equation a^(3)(x+5)^(2) - 25 a(x+5) + 50 = 0 , is

Find the number of real roots of the equation (x-1)^(2)+(x-2)^(2)+(x-3)^(2)=0

If the absolute value of the difference of the roots of the equation x^(2) + ax + 1 = 0 "exceeds" sqrt(3a) , then

real roots of equation x^(2)+3|x|+2=0 are

Find the number of real roots of the equation f(x) =x^(3) + 2x^(2) +x +2 =0

Write the number of real roots of the equation (x-1)^(2)+(x+2)^(2)+(x-3)^(2)=0