Home
Class 12
MATHS
Suppose the cubic x^(3)-px+q has three d...

Suppose the cubic `x^(3)-px+q` has three distinct real roots, where `pgt0` and `qgt0`. Then which one of the following holds?

A

The cubic has minima at `- sqrt((p)/(3))` and maxima at `sqrt((p)/(3))`

B

The cubic has minima at both `sqrt((p)/(3))` and `-sqrt((p)/(3))`

C

The cubic has maxima at both `sqrt((p)/(3))` and `-sqrt((p)/(3))`

D

The cubic has minima at `sqrt((p)/(3))` and maxima at `- sqrt((p)/(3))`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MAXIMA AND MINIMA

    MOTION|Exercise EXERCISE - 4 (LEVEL - II)|17 Videos

  • MAXIMA AND MINIMA

    MOTION|Exercise EXERCISE - 3|32 Videos

  • MATRICES

    MOTION|Exercise Exercise - 4 (Level-II)|28 Videos

  • METHOD OF DIFFERENTIATION

    MOTION|Exercise EXERCISE - 4 LEVEL -II|5 Videos

Similar Questions

Explore conceptually related problems

Suppose the cubic x^3-px+q has three distinct real roots when p lt 0 and p lt 0. then which one of the following holds ? (a) The cubic has minima at -sqrt(p/3) and maxima at sqrt(p/3) (b) The cubic has minima at both sqrt(p/3) and -sqrt(p/3) (c) The cubic has maxima at both sqrt(p/3) and -sqrt(p/3) (d) The cubic has minima at sqrt(p/3) and maxima -sqrt(p/3)

Suppose the cubic x^3-px+q has three real roots where pgt0 and qgt0 . Then which one of the following holds ?

Find the value of a if x^(3)-3x+a=0 has three distinct real roots.

If x^(2) - px + q = 0 has equal integral roots, then

Find the value of k if x^(3)-3x+a=0 has three real distinct roots.

If p and q are the roots of x^2 +px + q = 0 , then which one of the following is correct ?

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)=ax+b=0 has distinct real roots and x^(2)+a|x|+b=0 has only one real root,then which of the following is true? b=0,a>0 b.b=0,a 0,a<0 d.b(:0,a:)0

Let 'p' & 'q' be real numbers . Prove that the cubic y = x^(3) + p x + q has three distinct real roots, if 4 p^(3) + 27 q^(2) lt 0 .