If , where such that and ,…

MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series

Problem

If (1+ax+bx2)4=a0+a1x+a2x2+⋯+a8x8(1 + ax + bx^2)^4 = a_0 + a_1 x + a_2 x^2 + \dots + a_8 x^8 , where a,b,a0,a1,…,a8∈Ra, b, a_0, a_1, \dots, a_8 \in \mathbb{R} such that a0+a1+a2≠0a_0 + a_1 + a_2 \neq 0 and ∣a0a1a2a1a2a0a2a0a1∣=0\begin{vmatrix} a_0 & a_1 & a_2 \\ a_1 & a_2 & a_0 \\ a_2 & a_0 & a_1 \end{vmatrix} = 0 , then (1) a=34,b=58a = \frac{3}{4}, b = \frac{5}{8} (2) a=14,b=532a = \frac{1}{4}, b = \frac{5}{32} (3) a=1,b=23a = 1, b = \frac{2}{3} (4) None of these

Related theory

Browse the problem library