Question

Polynomials are everywhere. It is found in the slope of a hill, the curve of a bridge or the continuity of a mountain range.

Based on the given information, answer the following question.

If the hills are prepresented by the cubic polynomial $t\left(x\right)=2x^3+8x^2+9x+16,$ then the product of the zeroes is:

• A. $-4$
• B. $\frac{9}{2}$
• C. $-8$
• D. $8$

Answer 1

The correct option is C $-8$

To find: The product of the zeroes of the polynomial $t\left(x\right)=2x^3+8x^2+9x+16$

We know that, a general cubic polynomial can be written in the form of $x^3-(\alpha +\beta +\gamma )x^2+(\alpha \beta +\beta \gamma +\gamma \alpha )x-\alpha \beta \gamma$ where $\alpha ,\beta ,\gamma$ are the zeroes of the polynomial.

On comparing the given polynomial to its general form,
$t\left(x\right)=x^3+4x^2+\frac{9}{2}x+8$
Here, the negative of the constant term will be the product of the zeroes.
Hence, the required answer is $-8.$