The equation `2x ^(3) -3x ^(2) +p=0` has three real roots. Then find the minimum value of p.

If the equation 2x^(3) -6x + k=0 has three real and distinct roots, then find the value (s) of k.

If the equation x^(2)+(p^(2)+5)x-2p=0(p in R) has roots alpha,beta then find the minimum value of (1-alpha)(1-beta)

if the roots of the cubic x^(3)-12x^(2)+ax-64=0 are positive real numbers, then find the minimum value of a

If he equation x^(3)+ax^(2)+bx+216=0 has three real roots in G.P.then b/a has the value equal to

2x^(2) + 3x - alpha - 0 " has roots "-2 and beta " while the equation "x^(2) - 3mx + 2m^(2) = 0 " has both roots positive, where " alpha gt 0 and beta gt 0. It is given that the roots of the equation x^(2) - 4x - log_(3) P=0 are real . For this, the minimum value of P is

If 2x^(3)+ax^(2)+bx+4=0 has three real roots.The minimum value of a^(3) is The minimum value of b^(3) is.The inimum value of (a+b)^(3) is

Show that the equation 2x^(2)-6x+3=0 has real roots and find these roots.

If the roots of the quadratic equation 4x^(2) -16x + p = 0 , are real and unequal, then find the value/s of p.