Question

Find the zeros of the polynomial 2 x cube + 5 x square - 9 x minus 18 if it is given that the product of its two zeros is -3

Answer 1

the number 4 is the answer.

Answer 2

Answer:

The zeros of the polynomial are -3, -1.5, 2.

Step-by-step explanation:

The given polynomial is

$2x^3+5x^2-9x-18$

Let p, q, r are three roots.

The product of two roots is -3.

$pq=-3$                       ....(1)

The product of roots is -d/a.

$pqr=\frac{18}{2}$

$(-3)r=9$

$r=-3$

The sum of roots is -b/a.

$p+q+r=\frac{-5}{2}$

$p+q-3=\frac{-5}{2}$

$p+q=\frac{1}{2}$             .... (2)

On solving (1) and (2), we get

$\frac{-3}{q}+q=\frac{1}{2}$

$2q^2-q-6=0$

$(2q+3)(q-2)=0$

$q=-1.5,2$

The value of second root is either -1.5 and 2.

Put these value in (1).

$p=\frac{-3}{-1.5}=2$

$p=\frac{-3}{2}=1.5$

The value of first root is either 2 and -1.5 .

Therefore zeros of the polynomial are -3, -1.5, 2.