If the sum of the zeros of the polynomial f(x) = 2x³ − 3kx² + 4x − 5 is 6, find the value of k

Video Explanation

Watch the video explanation below:

Given

f(x) = 2x³ − 3kx² + 4x − 5

Sum of the zeros = 6

To Find

The value of k.

Solution

For a cubic polynomial of the form:

ax³ + bx² + cx + d

Sum of zeros = −b/a

Step 1: Identify a and b

Comparing f(x) = 2x³ − 3kx² + 4x − 5 with ax³ + bx² + cx + d:

a = 2
b = −3k

Step 2: Use the Formula for Sum of Zeros

Sum of zeros = −b/a

= −(−3k)/2

= 3k/2

Step 3: Given Sum = 6

3k/2 = 6

3k = 12

k = 4

Final Answer

The value of k is:

k = 4

Correct Option

(b) 4

Conclusion

Hence, if the sum of the zeros of the polynomial f(x) = 2x³ − 3kx² + 4x − 5 is 6, then the value of k is 4.