Question

if two zeros of the polynomial x^4 + 3 x^3 - 20 x^2- 6 X + 36 are √2 and -√2 find other zeros of the polynomial.

Answer 1

Uh can find this by using this method....

Hope this may helpful for you...

Answer 2

Hey

Here is your answer,

Let p(x) = x4+3x3 - 20x2 - 6x+36
Given √2 and -√2 are the zeroes of the polynomial.
Hence (x + √2) and (x - √2) are the factors of the given polynomial.
(x + √2)(x - √2) = x2 2
On dividing (x4+3x3 - 20x2 - 6x+36) with (x2 2) we the quotient as (x2 +3x 18)
∴ (x4+3x3 - 20x2 - 6x+36) = (x2 -2) (x2 +3x - 18)
= (x2 - 2) (x2 +6x -3x - 18)
= (x2 - 2) [x(x +6) - 3(x -6)]
= (x2 - 2)(x +6)(x - 3)
∴ (x +6)(x -3) = 0
⇒ (x +6)= 0 and (x - 3) = 0
⇒ x = - 6 and x = 3
Therefore the other zeroes are 3 and -6.

Hope it helps you!
Mark brainliest plzz...