Home
Class 12
MATHS
Find the value of k if x^3-3x+a=0 has th...

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

Text Solution

AI Generated Solution

To find the value of \( a \) such that the equation \( x^3 - 3x + a = 0 \) has three distinct real roots, we can follow these steps: ### Step 1: Analyze the function We start with the function: \[ f(x) = x^3 - 3x + a \] We need to determine the conditions under which this cubic function has three distinct real roots. ...
Promotional Banner

Topper's Solved these Questions

  • GRAPHS OF POLYNOMIAL AND RATIONAL FUNCTIONS

    CENGAGE ENGLISH|Exercise Exercises|17 Videos

  • GRAPHICAL TRANSFORMATIONS

    CENGAGE ENGLISH|Exercise ILLUSTRATION|78 Videos

  • GRAPHS OF ELEMENTARY FUNCTIONS

    CENGAGE ENGLISH|Exercise EXERCISES|34 Videos

Similar Questions

Explore conceptually related problems

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

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

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

If the equation 2x^(3) -6x + k=0 has three real and distinct roots, then find the value (s) of k.

Draw the graph of f(x)=log_(e)(sqrt(1-x^(2))) .Find the range of the function .Also find the values of k if f(x) has two distinct real roots.

Find the values of k for which the equation x^2-4x+k=0 has distinct real roots.

If f(x) is a real valued polynomial and f (x) = 0 has real and distinct roots, show that the (f'(x)^(2)-f(x)f''(x))=0 can not have real roots.

Let x^(2) - ( m - 3) x + m = 0 ( m in R) be a quadratic equation. Find the value of m for which the roots are (i) real and distinct (ii) equal (iii) not real

If the function f(x)=x^(3)-9x^(2)+24x+c has three real and distinct roots alpha, beta and gamma , then the value of [alpha]+[beta]+[gamma] is

Find the value of k for which the equation 3x^(2)-6x+k=0 has distinct and real root.