Question

if the product of two zeroes of polynomial 2x^3+3x^2-5x-6 is 3,find its third zero

Answer 1

Answer:

The third zero=c=1

Step-by-step explanation:

The given polynomial is= $2x^{3}+3x^{2}-5x-6$, and the product of two zeroes is =3.

Let a, b and c are the three zeroes of the given polynomial, then ab=3...........(1), also, product of the zeroes=$-\frac{d}{a}=-\frac{-6}{2}=3$......(2)

From, (1) and (2), we get

$\frac{ab}{abc}=\frac{3}{3}$

$c=1$

Therefore, the third zero=c=1

Answer 2

Answer:

The given polynomial is= 2x^{3}+3x^{2}-5x-62x

3

+3x

2

−5x−6 , and the product of two zeroes is =3.

Let a, b and c are the three zeroes of the given polynomial, then ab=3...........(1), also, product of the zeroes=-\frac{d}{a}=-\frac{-6}{2}=3−

a

d

=−

2

−6

=3 ......(2)

From, (1) and (2), we get

\frac{ab}{abc}=\frac{3}{3}

abc

ab

=

3

3

c=1c=1

Therefore, the third zero=c=1