|向量a|=3|向量b|≠0,2x²＋2|向量a|x＋3向量a向量b=0有实根,则向量a向量b的夹角取值范围A[0,π/6]B[π/3,π][π/3,π2/3]D[π/6,π]

|向量a|=3|向量b|≠0,2x²＋2|向量a|x＋3向量a向量b=0有实根,则向量a向量b的夹角取值范围A[0,π/6]B[π/3,π][π/3,π2/3]D[π/6,π]
|向量a|=3|向量b|≠0,2x²＋2|向量a|x＋3向量a向量b=0有实根,则向量a向量b的夹角取值范围A[0,π/6]
B[π/3,π][π/3,π2/3]D[π/6,π]

|向量a|=3|向量b|≠0,2x²＋2|向量a|x＋3向量a向量b=0有实根,则向量a向量b的夹角取值范围A[0,π/6]B[π/3,π][π/3,π2/3]D[π/6,π]
2x²＋2|向量a|x＋3向量a向量b=0有实根
则判别式=(2|向量a|)²-4*2*3向量a.向量b≥0
∴ 4|a|²-24|a|*|b|*cosA≥0
代入3|b|=|a|
∴ 4|a|²-8|a|²cosA≥0
∴ cosA≤1/2
∵ A ∈[0,π]
∴ π/3≤A≤π
选B