Question

Find all the zeroes of the polynomial 2x4-3x3-3x2+6x-2, if two of its zeroes are
√2 and -√2

Answer 1

EXPLANATION.

Zeroes of the polynomial.

⇒ 2x⁴ - 3x³ - 3x² + 6x - 2.

If two zeroes are √2  and  -√2.

As we know that,

Zeroes of the polynomial.

⇒ x = √2.

⇒ x - √2 = 0. - - - - - (1).

⇒ x = -√2.

⇒ x + √2 = 0. - - - - - (2).

Products of the zeroes of the quadratic equation.

⇒ (x - √2)(x + √2).

As we know that,

Formula of :

⇒ (x² - y²) = (x - y)(x + y).

Using this formula in the equation, we get.

⇒ x² - 2.

Divide :

⇒ 2x⁴ - 3x³ - 3x² + 6x - 2  by  x² - 2.

We get,

⇒ 2x² - 3x + 1.

Factorizes the equation into middle term splits, we get.

⇒ 2x² - 2x - x + 1 = 0.

⇒ 2x(x - 1) - 1(x - 1) = 0.

⇒ (2x - 1)(x - 1) = 0.

⇒ x = 1/2  and  x = 1.

All the zeroes of the polynomial = √2, -√2, 1/2, 1.

Answer 2

Answer:

,

Step-by-step explanation:

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