Question

if the product of zeroes of the polynomial ax³+bx²+cx+d is 1 then find the value of a​

Answer 1

Given

A polynomial ax³+bx²+CX+d

whose product of zeroes = 1

To find

Value of a

Solution

Let the zeroes of the polynomial be $\alpha,\beta\:and\gamma=\frac{-b}{a}$

$\alpha+\beta+\gamma=\frac{-b}{a}$

$\alpha.\beta+\beta.\gamma+\gamma.\alpha=\frac{c}{a}$

$\alpha.\beta.\gamma=\frac{-d}{a}$

Now

• product of zeroes

$\alpha.\beta.\gamma=\frac{-d}{a}$

Putting the value of

d and a

$\alpha.\beta.\gamma=\frac{-d}{1}$

$\implies1=\frac{-1}{a}$

$\therefore\:a=-1$