Question

find all the zeroes of the polynomial f(x)=2x⁴-3x³-3x²+6x-2, if two of its zeros are √2 and -√2​

Answer 1

Answer:

Given √2 and -√2 are two zeroes.

So (x - √2) and (x - -√2) are the factors.

i. e., (x - √2) & (x + √2) are the factors.

So, (x - √2)(x + √2)is also a factor.

i. e., x²- (√2)² = x² - 2 is a factor.

_2x² _- _3x_+_1_____

x² - 2 |2x⁴ - 3x³ - 3x² + 6x - 2

|2x⁴ - 4x²

|__________________

| - 3x³ + x² + 6x - 2

| - 3x³ + 6x

|__________________

x² - 2

x² - 2

__________________

0

2x² - 3x + 1

a + b = -3

a × b = 2

-1 + -2 = -3

-1 × -2 = 2

2x² - 3x + 1 = 0

2x² - 2x - 1x + 1 = 0

2x(x - 1) - 1(x - 1) = 0

(2x - 1)(x- 1) = 0

2x - 1 = 0 OR x - 1 = 0

2x = 1 x = 1

x = 1/2

I hope this will help u. Please mark me as a brainliest.

Answer 2

Step-by-step explanation:

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