If the product of the zeros of the polynomial f(x) = ax³ − 6x² + 11x − 6 is 4, find the value of a

Video Explanation

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Given

f(x) = ax³ − 6x² + 11x − 6

Product of the zeros = 4

To Find

The value of a.

Solution

For a cubic polynomial:

ax³ + bx² + cx + d

Product of zeros = −d / a

Step 1: Identify a and d

Comparing f(x) = ax³ − 6x² + 11x − 6 with ax³ + bx² + cx + d,

a = a,   d = −6

Step 2: Use the Formula for Product of Zeros

Product of zeros = −d / a

= −(−6) / a

= 6 / a

Step 3: Use the Given Condition

6 / a = 4

6 = 4a

a = 3/2

Final Answer

a = 3/2

Conclusion

Hence, if the product of the zeros of the polynomial f(x) = ax³ − 6x² + 11x − 6 is 4, then the value of a is 3/2.