Finding the Value of k Using Sum of Zeroes

Video Explanation

Question

If the sum of the zeroes of the polynomial

\[ f(x) = 2x^3 – 3kx^2 + 4x – 5 \]

is \(6\), then find the value of \(k\).

Options:

(a) 2    (b) 4    (c) -2    (d) -4

Solution

Step 1: Use the Formula for Sum of Zeroes

For a cubic polynomial \[ ax^3 + bx^2 + cx + d, \]

the sum of zeroes is given by:

\[ -\frac{b}{a} \]

Step 2: Compare with the Given Polynomial

Given polynomial:

\[ 2x^3 – 3kx^2 + 4x – 5 \]

Here,

\[ a = 2, \quad b = -3k \]

Step 3: Substitute the Given Sum of Zeroes

\[ -\frac{-3k}{2} = 6 \]

\[ \frac{3k}{2} = 6 \]

\[ 3k = 12 \Rightarrow k = 4 \]

Conclusion

The correct value of \(k\) is:

\[ \boxed{4} \]

Hence, the correct option is (b) 4.