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.
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
x4−16x3+86x2−176x+105 −8x3+79x2−176x+105 15x2−120x+105 0
Quotient is x2−8x+15
Correct option : D