If a, b `in` R, then the equation `x^(2) - abx - a^(2) = 0` has

If a, b in R , and the equation x^(2) + (a - b) x - a - b + 1 = 0 has real roots for all b in R , then a lies in the in terval

If a, b, c in R and 2a + 3b + 6c = 0, then the equation ax^(2) + bx + c = 0 has

If (1)/(sqrt(alpha)) and (1)/(sqrt(beta)) are the roots of equation ax^(2)+bx+1=0(a!=0,(a,b in R)), then the equation x(x+b^(3))+(a^(3)-3abx)=0 has roots -

If 2 a+3 b+6 c=0, a, b, c in R then the equation a x^(2)+b x+c=0 has a root in

If a,b in R and the equation x^(2)+(a-b)x+1-a-b=0 has unequal roots for all b in R then a can be

If a,b,c in R and the quadratic equation x^(2)+(a+b)x+c=0 has no real roots then

The roots of the equation 2a^(2)x^(2) - 2abx + b^(2) = 0 when a lt 0 and b gt 0 are :