Question

The product of the zeroes of a polynomial \(x^3 - 3x^2 + x + 1\) is:

• A. 1
• B. -1
• C. 3
• D. -3

Hint:

To find the product of the zeroes of a cubic polynomial, use the formula \( \alpha \beta \gamma = -\frac{d}{a} \).

Answer 1

The Correct Option is B

For a cubic polynomial of the form \( ax^3 + bx^2 + cx + d \), the product of its zeroes \( \alpha, \beta, \gamma \) is given by the relation: \[ \alpha \beta \gamma = -\frac{d}{a} \] For the polynomial \( x^3 - 3x^2 + x + 1 \), the coefficients are:
\( a = 1 \)
\( b = -3 \)
\( c = 1 \)
\( d = 1 \)
Using the formula for the product of the zeroes: \[ \alpha \beta \gamma = -\frac{1}{1} = -1 \] Thus, the product of the zeroes is \( -1 \).