Product of Zeroes of a Cubic Polynomial

Video Explanation

Question

The product of the zeroes of the polynomial

\[ f(x) = x^3 + 4x^2 + x – 6 \]

is:

(a) -4    (b) 4    (c) 6    (d) -6

Solution

Step 1: Use the Formula for Product of Zeroes

For a cubic polynomial

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

the product of its zeroes is given by

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

Step 2: Apply to the Given Polynomial

Here,

\[ a = 1, \quad d = -6 \]

So, the product of the zeroes is:

\[ -\frac{-6}{1} = 6 \]

Conclusion

The product of the zeroes is:

\[ \boxed{6} \]

Hence, the correct option is (c) 6.