Question

If the product of two zeros of polynomial 2x³+3x²-5x-6 is 3, then find its third zero.

Answer 1

Step-by-step explanation:

Given the polynomial

P(x)=2x^3+3x^2-5x-6

The product of two zeroes is 3 we have to find the third zero

P(x)=2x^3+3x^2-5x-6

\text{Product of zeroes is }\frac{-d}{a}=-(\frac{-6}{2})=3

abc=3

As product of two zeroes is 3

Let ab=3

Therefore,

3c=3

⇒ c=1

hence, the third zero is 1.

Answer 2

Comparing the equation with

ax³+bx²+cx+d =0

a=2 ,b=3,c=-5 and d= -6

$\alpha \beta \gamma = \frac{ - d}{a} \\ 3 \gamma = - (\frac{ - 6}{2} ) \\ 3 \gamma = 3 \\ \gamma = 1$