DeterminantHard

Question

If  = ax3 + bx, then -

Options

A.a = 4, b = 2
B.a = 4, b = -2
C.a = -2, b = 4
D.None of these

Solution

= ax3 + bx
=
= ax3 + bx

= ax3 + bx
4x3 + 4x5 + 8x7 + 8x9 + 8x11 - 2x - 2x5 - 2x9 - 4x3 - 4x11
= (ax3 + bx) (1 + x4 + x8 + 2x6 + 2x2 + 2x4)
Comparing the coefficient
coeff. of x3   ....... (1)
Coeff. of x9  8 - 2 = 2a + b
2a + b = 6                ....... (2)
Solve equations (1) and (2)
a = 4, b = - 2

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