Question

The product of zeroes of the cubic polynomial $2x^3-5x^2-14x+8$ is

• A. 25
• B. 4
• C. -7
• D. -4

Answer 1

The correct option is D -4

The sum and product of the zeroes of the polynomial are $2.5$ and $-4$ respectively.
Step-by-step explanation:
The given polynomial
$$p\left(x\right)=2x^3-5x^2-14x+8$$
If a three degree polynomial is $f\left(x\right)=a{x}^3+b{x}^2+cx+d$, then
Sum of zeroes $=-b/a$
Product of zeroes $=-d/a$
In the given polynomial $a=2,b=-5,c=-14$ and $d=8$.
Sum of zeroes $=-(-5)/\left(2\right)=2.5$
Product of zeroes $=-\left(8\right)/\left(2\right)=-4$
Therefore, the sum and product of the zeroes of the polynomial are $2.5$ and $-4$ respectively.