Question

Find all the zeroes of the polynomial x^4+2x^3-17x^2-4x+30, given that two zeroes are 3 and - 5​

Answer 1

Answer:

Given zeroes are 1 and 2

So, (x – 3)and [x – (-5)] are the factors of x4 + 2x3 – 17x2 – 4x + 30

⇒ (x – 3)(x + 5)

= x2 + 5x – 3x – 15

= x2 + 2x – 15 is a factor of given polynomial.

Consequently, x2 + 2x – 15 is also a factor of the given polynomial.

Now, let us divide x4 + 2x3 – 17x2 – 4x + 30 by x2 + 2x – 15

The division process is

not given here

you have to solve yourself❤

Here, quotient = x2 – 2

= (x – 2)(x + 2)

So, the zeroes are -2 and 2

Hence, all the zeroes of the given polynomial are -2, 2, 3 and 5.

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