Question

Find the zeros of the polynomial 2x³ + 5x² -9x - 18 if it is given that the product of its two zeroes is -3

Answer 1

the solution in the pictures and the zeros are
-3,2,-3/2
hope it is help ful

Answer 2

Answer:

-3, -1.5 and 2

Step-by-step explanation:

The given polynomial is

$P(x)=2x^3 + 5x^2 -9x - 18$

If l,m and n are three zeors of the polynomial $P(x)=ax^3+bx^2+cx+d$, then

$l+m+n=-\frac{b}{a}$            ... (1)

$lm+mn+ln=\frac{c}{a}$       .... (2)

$lmn=\frac{d}{a}$        .... (3)

In the given polynomial a=2, b=5, c=-9 and d=-18.

It is given that the product of its two zeroes is -3.

Let three zeroes of the given polynomial are l, m and n.

$lm=-3$                  .... (4)

Using equation (3) we get

$lmn=-\frac{-18}{2}$

$(-3)n=9$

Divide both sides by -3.

$n=-3$

The value of n is -3 it means the third zero is -3.

Using (1) we get

$l+m-3=-\frac{5}{2}$

$l+m=-\frac{5}{2}+3$

$l+m=\frac{1}{2}$            ... (5)

On solving (4) and (5) we get

$l=-1.5, 2$

Substitute the value of l in equation (4).

m=2 at l=-1.5 and m=-1.5 at l=2.

Therefore the zeroes of the polynomial are -3, -1.5 and 2.