Let a,b,c∈R with a > 0 such that the equation ax2+bcx+b3+c3−4abc=0 has non-real roots.If P(x)=ax2+bx+c and Q(x)=ax2+cx+b, then

Given equation has non-real roots.∴     D<0⇒    b2c2−4b3+c3−4abca<0⇒    b2c2−4ab3+16a2bc−4ac3<0⇒    b2c2−4ab−4acc2−4ab<0⇒    b2−4acc2−4ab<0⇒    DP(x)⋅DQ(x)<0Therefore, exactly one of P(x) or Q(x) is positive for all real x.