Roots are real only when D is non-negative.

Roots are equal only when D =0.

Roots are rational only when D is a perfect square number like 0,1,4,9,16,….. Etc.

Roots are complex (or imaginary) when D is negative.

Let f(x)=ax^3+bx^2+x+d has local extrema at x=alpha and beta such that alphabetalt0 and f(alpha).f(beta)gt0 . Then the equation f(x)=0 (A) has 3 distinct real roots (B) has only one real which is positive o a.f(alpha)lt0 (C) has only one real root, which is negative a.f(beta)gt0 (D) has 3 equal roots

If the equation x^(2)-2px+q=0 has two equal roots, then the equation (1+y)x^(2)-2(p+y)x+(q+y)=0 will have its roots real and distinct only, when y is negative and p is not unity.

Equation x^4ax^3+bx^2+cx+1=0 has real roots (a,b,c are non-negative). Minimum non-negative real value of a is

Equation x^4ax^3+bx^2+cx+1=0 has real roots (a,b,c are non-negative). Minimum non-negative real value of b is

Equation x^4+ax^3+bx^2+cx+1=0 has real roots (a,b,c are non-negative). Minimum non-negative real value of c is

The number of roots of the equation z^(6)=-64 whose real parts are non-negative,

The equation 7xx^(2)-(7pi+22)xx+22pi=0has (A) equal roots (B) a root which is negative (C) rational roots only (D) a rational root and an irrational root.