Question

Find all the zeroes of the polynomial x4 – 8x3 + 23x2 – 28x + 12 if two of


its zeroes are 2 and 3.​

Answer 1

Answer:

hope this helps you

Step-by-step explanation:

Answer :

Given zeroes are 1 and 2

So, (x – 1)and (x – 2) are the factors of x4 – 8x3 + 23x2 – 28x + 12

⟹ (x – 1)(x – 2) = x2 – 3x + 2 is a factor of given polynomial.

Consequently, x2 – 3x + 2 is also a factor of the given polynomial.

Now, let us divide x4 – 8x3 + 23x2 – 28x + 12 by x2 – 3x + 2

The division process is

Here, quotient = x2 – 5x + 6

= x2 – 2x – 3x + 6

= x(x – 2) – 3(x – 2)

= (x – 3)(x – 2)

So, the zeroes are 3 and 2

Hence, all the zeroes of the given polynomial are 1, 2 ,2 and 3.