Finding the Value of a Using Product of Zeroes

Video Explanation

Question

If the product of the zeroes of the polynomial

\[ f(x) = ax^3 – 6x^2 + 11x – 6 \]

is \(4\), find the value of \(a\).

Solution

Step 1: Use the Formula for Product of Zeroes

For a cubic polynomial

\[ ax^3 + bx^2 + cx + d, \]

the product of the zeroes is given by

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

Step 2: Compare with the Given Polynomial

Given polynomial:

\[ ax^3 – 6x^2 + 11x – 6 \]

Here,

\[ a = a,\quad d = -6 \]

Step 3: Substitute the Given Product of Zeroes

\[ -\frac{-6}{a} = 4 \]

\[ \frac{6}{a} = 4 \]

\[ a = \frac{6}{4} = \frac{3}{2} \]

Conclusion

The value of \(a\) is:

\[ \boxed{\frac{3}{2}} \]