Let p(x)=x^2+ax+b have two distinct real...

Let p(x)=`x^2+ax+b` have two distinct real roots, where a, b are real numbers. Define g(x)=`p(x^3)` for all real numbers x. Then which of the following statements are true?
I. g has exactly two distinct real roots.
II. g can have more than two distinct real roots
III. There exists a real number `alpha` such that g(x) `ge alpha` for all real x

A

Only I

B

Only I and III

C

Only II

D

Only II and III

AI Generated Solution

Similar Questions

Explore conceptually related problems

Which of the following graphs has more than three distinct real roots?

Which of the following equations has two distinct real roots ?

If a and b are two distinct real roots of the polynomial f(x) such that a

Which of the following equations has two distinct real roots?

If the equation ax^(2)+bx+c=0 has distinct real roots and ax^(2)+b{x}+C=0 also has two distinct real roots then

If the equation sin ^(2) x - k sin x - 3 = 0 has exactly two distinct real roots in [0, pi] , then find the values of k .

If g(x)="min"(x,x^(2)) , where x is a real number, then

Let f(x)=(e^(x))/(x^(2))x in R-{0}. If f(x)=k has two distinct real roots,then the range of k, is

State whether the following quadratic equations have two distinct real roots. Justicy your answer: (x+1)(x-2)+x=0