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\left. \begin array l \text polynomial 2 x ^ 4 - 11 x ^ 3 %2B 7 x ^ 2 %2B 13 x - \\ ( 3 %2B \sqrt 2 ) \text and ( 3 - \sqrt 2 ) \end array \right. |
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Answer» If α and β are zeroes of the polynomial 2x⁴ - 11x³ + 7x² + 13x - 7 Then, x² - (α + β)x + αβ . Here, α = (3 + √2) andβ = (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 . Like my answer if you find it useful! |
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