Question

find all the zeros of 2x⁴- 3x³-3x²+6x2 if its zeros are root 2 and -2 root.??
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Answer 1

EXPLANATION.

All the zeroes of the polynomials,

⇒ 2x⁴ - 3x³ - 3x² + 6x - 2.

If its zeroes are √2 and -√2.

As we know that,

Zeroes of polynomials,

⇒ x = √2.

⇒ x - √2.

⇒ x = - √2.

⇒ x + √2.

As we know that,

Products of the zeroes.

⇒ (x - √2)(x + √2).

As we know that,

Formula of :

⇒ (x² - y²) = (x - y)(x + y).

⇒ (x² - 2).

Divide :

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

We get.

⇒ 2x² - 3x + 1.

Now we 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 zeroes of the polynomials are,

⇒ √2 , -√2 , 1/2 , 1.

                                                                                                                     

MORE INFORMATION.

Conjugates roots.

(1) = If D < 0.

One roots = α + iβ.

Other roots = α - iβ.

(2) = If D > 0.

One roots = α + √β.

Other roots = α - √β.

Answer 2

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All the zeroes of the polynomials,

⇒ 2x⁴ - 3x³ - 3x² + 6x - 2.

If its zeroes are √2 and -√2.

As we know that,

Zeroes of polynomials,

⇒ x = √2.

⇒ x - √2.

⇒ x = - √2.

⇒ x + √2.

As we know that,

Products of the zeroes.

⇒ (x - √2)(x + √2).

As we know that,

Formula of :

⇒ (x² - y²) = (x - y)(x + y).

⇒ (x² - 2).

Divide :

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

We get.

⇒ 2x² - 3x + 1.

Now we 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 zeroes of the polynomials are,

⇒ √2 , -√2 , 1/2 , 1.

                                                                                                                     

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