If the equation `x^(2)+2ax+b(a-1)=0` has real roots for all real value of a and `b` is an integer, then

Show that the equation x^(2)+ax-4=0 has real and distinct roots for all real values of a .

The quadratic equation ax^(2)+bx+c=0 has real roots if:

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^(3)-9x^(2)+12x-5=0 has two equal real roots then sum of all values of a is

Show that the roots of the equation x^(2)+px-q^(2)=0 are real for all real values of p and q.

If the equation ax^(2) + 2 bx - 3c = 0 has no real roots and (3c)/(4) lt a + b , then

If a and b are positive real numbers and each of the equations x^(2)+3ax+b=0 and x^(2)+bx+3a=0 has real roots,then the smallest value of (a+b) is

If the equation ax^(2)+2bx+c=0 has real roots, a,b,c being real numbers and if m and n are real numbers such that m^(2)gtngt0 then prove that the equation ax^(2)+2mbx+nc=0 has real roots.

If the equation ax^(2)+bx+c=x^(3)+(1)/(x)(a.b.c<=0) has only real roots and all the roots are integers then the value of (-a-b-c)/(7) is