Question

If the sum of zeroes of a given polynomial f(x) =x3 - 3k x3-x+30 is 6 find the value of k.

Answer 1

hey
________

ans = 2

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Answer 2

Answer:

The value of k = 2

Step-by-step explanation:

Given,

The sum of roots of the equation $f(x) =x^3 - 3kx^2-x+30$ is 6

To find,

The value of 'k'

Recall the concept

If $\alpha\ \beta \ \gamma$ are the roots of the cubic equation $ax^3+bx^2+cx+d = 0$,

then sum of roots $\alpha\ + \beta \ + \gamma = \frac{-b}{a}$

Solution:

Comparing the given equation $f(x) =x^3 - 3kx^2-x+30$ with $ax^3+bx^2+cx+d$ we get

a = 1

b = -3k

Then, sum of roots of $f(x) =x^3 - 3kx^2-x+30$  = $\frac{-b}{a}$ = -(-3k) = 3k

Given that the sum of roots of  $f(x) =x^3 - 3kx^2-x+30$ = 6

Then we have 3k = 6

k = 2

∴The value of k = 2

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