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Question

Write bi-quadratic polynomial x416x3+86x2176x+105 as a product of two quadratic polynomial If one quadratic polynomial has roots  1 and 7.



A

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B

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C

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D

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Solution

The correct option is D


Quadratic polynomial if roots being 1 and 7 = (x - 1) (x -7) =  x2 - 8x + 7

If 1 and 7 are the roots of the given equation. (x - 1)(x - 7) are the factors of  x416x3+86x2176x+105=0.

Divide   x416x3+86x2176x+105 by x28x+7 and find the quotient

x2+8x+15                      x28x+7x416x3+86x2176x+105                                      _x4_+8x3_+7x2                                                         8x3+79x2176x+105                                                        +8x3 +64x2 +56x                                                        15x2120x+105                                                            _15x2+_+120x +105                                                       0                               
Quotient is  x28x+15

x416x3+86x2176x+105=(x28x+7)×(x28x+15)

Correct option : D


Mathematics

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