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

# If The Function f (x) = x3 – 9x2 + 24x + C Has Three Real And Distinct Roots α, β and γ then The Value Of [α] + [β] + [γ] Is,:

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## Question

### 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))

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Q6

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Q7

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Q8

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

Q9

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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.