Question

find all the zeros of polynomial 2x⁴- 11x³ + 7x²+ 13x-7 if two of its zeros are (3 + √2) and (3-√2)

Answer 1

★ BI-QUADRATIC EQUATION ★

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If α and β are zeroes of the polynomial 2x⁴ - 11x³ + 7x² + 13x - 7

Then, x² - (α + β)x + αβ .

Here, α = (3 + √2) and β = (3 - √2).

So, α+ β = 6 and  αβ = 7.

Thus, x² - 6x + 7 is a factor of 2x⁴ - 11x³ + 7x² + 13x - 7

Now, Given polynomial 2x⁴ - 11x³ + 7x² + 13x - 7, 


         So,                  x² - 6x + 7 ) 2x⁴ - 11x³ + 7x² + 13x - 7 ( 2x² + x - 1

                                                    2x⁴ - 12x³ + 14x²  (substract)
                                                  -----------------------------
                                                            x³ - 7x² + 13x
                                                            x³ -  6x² + 7x   (substract)
                                                           --------------------------------------
                                                                 - x² + 6x - 7
                                                                 - x² + 6x - 7  (substract)
                                                                -----------------------------
                                                                             0
                                                                -----------------------------

We have, the Quotient as 2x² + x -1

                                      = 2x² + 2x - x  -1

                                      = 2x(x + 1) - 1(x + 1)
 
                                      = (2x - 1)(x + 1)

∴ x = 1/2 , -1 are the other zeros of the polynomial .

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#REDRAGON

Answer 2

Step-by-step explanation:

hey guyz

here is your answer

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