The equation `x^3 + px^2-px-1=0` has three distinct real roots if `p in (-oo,lambda)uu(mu, oo)`. then `|lambda+mu|` is equal to

The quadratic equation 2x^(2) + px + 3 = 0 has two equal roots if p = ______

If the equation 3x^(3)+2x^(2)-5x+lambda=0 ,has two distinct and real roots in [0,1] ,then the values lambda can take are

The quadratic equation 2x^(2) + px + 3 = 0 has two equal roots if p = …………. .

The quadratic equation (a+3)x^(2)-ax+1=0 has two distinct real solutions a) for a in(-2,6) b) for a in(-oo,0)uu(7,oo) c) for a in(-oo,-2)uu(6,oo)-{-3} d) for a in(0,7)

If the equation x^(3) +px +q =0 has three real roots then show that 4p^(3)+ 27q^(2) lt 0 .

If the equation x^(3) +px +q =0 has three real roots then show that 4p^(3)+ 27q^(2) lt 0 .