Question

# Write bi-quadratic polynomial x4−16x3+86x2−176x+105 as a product of two quadratic polynomial If one quadratic polynomial has roots  1 and 7.

A

B

C

D

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  x4−16x3+86x2−176x+105=0. Divide   x4−16x3+86x2−176x+105 by x2−8x+7 and find the quotient x2+8x+15                      x2−8x+7x4−16x3+86x2−176x+105                                      _x4_+−8x3_−+7x2                                                         −8x3+79x2−176x+105                                                        +−8x3 −+64x2 +−56x                                                        15x2−120x+105                                                            _−15x2+_+120x −+105                                                       0                                Quotient is  x2−8x+15 x4−16x3+86x2−176x+105=(x2−8x+7)×(x2−8x+15) Correct option : DMathematics

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