TMUA Official Specimen Paper 2 · Question 19

The positive real numbers $a$ , $b$ , and $c$ are such that the equation

x^3+ax^2=bx+c

has three real roots, one positive and two negative.

Which one of the following correctly describes the real roots of the equation

x^3+c=ax^2+bx?

AIt has three real roots, one positive and two negative.

BIt has three real roots, two positive and one negative.

CIt has three real roots, but their signs differ depending on

a

b

, and

c

DIt has exactly one real root, which is positive.

EIt has exactly one real root, which is negative.

FIt has exactly one real root, whose sign differs depending on

a

b

, and

c

GThe number of real roots can be one or three, but the number of roots differs depending on

a

b

, and

c

examday