Find `a` for which `x^2+(a-b)x+(1-a-b)=` has two distinct real roots for `AA b in R`

Let a b be arbitary real numbers Find the smallest natural number b for which equation x^(2)+2(a+b)x+(a-b+8)=0 has unequal real roots for all a in R .

Let a b be arbitrary real no.Find the smallest natural no.b for which the equation x^(2)+2(a+b)x+(a-b+8)=0 has unequal real roots for all a in R

Let a b be arbitrary real no.Find the smallest natural no.b for which the equation x^(2)+2(a+b)x+(a-b+8)=0 has unequal real roots for all a in R

The equation |x-a|-b|=c has four distinct real roots,then

If a x^2+(b-c)x+a-b-c=0 has unequal real roots for all c in R ,then

If a x^2+(b-c)x+a-b-c=0 has unequal real roots for all c in R ,then

If a x^2+(b-c)x+a-b-c=0 has unequal real roots for all c in R , then

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 the equation ax^(2)+bx+c=0 has distinct real roots and ax^(2)+b{x}+C=0 also has two distinct real roots then

Set of all value of 'a for which the equation (a+1)x^(2)+2bax+(a+1)b=0 has real and distinct roots for all b in R is