Question

If the function f (x) = x3 – 9x2 + 24x + c has three real and distinct roots αβ and γ then the value of [α] + [β] + [γ] is,:

Solution

Correct option is

7, 8

Take y = x3 – 9x2 + 24x = x (x2 – 9x + 24)   

         y = x(x2 – 9x + 24) = x {(x – 3)2 + 15} 

                    

For three real roots of 

        f (x) = x3 – 9x2 + 24x + cc must lie in the interval (–20, –16)

Now if c Ïµ (–20, –18)   

                                  

 

                          

  

SIMILAR QUESTIONS

Q1

Let f : [2, 7] and [0, ) be a continuous and differentiable function.

Then the value of (f (7) – f (2))  is (where c Ïµ (2, 7))

Q2

The equation sin x + x cos x = 0 has at least one root in the interval

Q3

Let f (x) = ax5 + bx4 + cx3 + dx2 + ex, where abcde Ïµ R and f (x) = 0 has a positive root α, then 

Q4

Between any two real roots of the equation ex sin x – 1 = 0, the equation excos x + 1 = 0 has

Q5

f (x) is a polynomial of degree 4 with real coefficients such that f (x) = 0 is satisfied by x = 1, 2, 3 only, then f’(1). f’(2). f’(3) is equal to:

Q6

If f (x) is a polynomial of degree 5 with real coefficients such that  has 8 real roots then f (x) = 0 has:

Q7

If the function f (x) = | x2 + a | x | +b| has exactly three points of non-differentiability, then which of the following can be true?

Q8

If f (x) = loge x and g(x) = x2 and c Ïµ (4, 5), then  is equal to:

Q9

If the equation  has four solution then be lies in:

Q10

If at each point of the curve y = x3 – ax2 + x + 1 the tangents is inclined at an acute angle with the positive direction of the x-axis, a lies in the interval.