Math, asked by meghana4595, 1 year ago

if 2 + root 3 and 2 minus root 3 are the two zeros of the polynomial 2 X ^ 4 - 9 x cube + 5 x square + 3 x minus 1 is equal to zero obtain other two zeros​

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Answered by Sudin
67
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Answered by amitnrw
27

1 & -1/2 are other zeroes if  (2 + √3)  & (2 - √3)  are two Zeroes  of 2x⁴ - 9x³ + 5x² + 3x - 1

Step-by-step explanation:

if (2 + √3)  & (2 - √3)  are two Zeroes

=> (x - (2 + √3))(x - (2 - √3)) is a factor of 2x⁴ - 9x³ + 5x² + 3x - 1

x² -x(2 + √3 + 2 - √3)  + (4 - 3)

= x² - 4x  + 1

                                    2x² - x -1

     x² - 4x  + 1        _|  2x⁴ - 9x³ + 5x² + 3x - 1  |_

                                    4x⁴ - 8x³ + 2x²

                                   _________________

                                            -x³ + 3x² + 3x - 1

                                            -x³ + 4x²  - x

                                             ________________

                                                     -x² + 4x - 1

                                                      -x² + 4x - 1

                                                      ____________

                                                              0

2x⁴ - 9x³ + 5x² + 3x - 1  = ( x² - 4x  + 1) (2x² - x -1)

2x² - x -1 = 0

=> 2x² - 2x + x - 1 = 0

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

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

=> x = -1/2  & x = 1

1 & -1/2 are other zeroes

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