若(x²+px+q)(x²-2x-3)展开后不含x²,x³,求p、q的值
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/30 15:21:38
![若(x²+px+q)(x²-2x-3)展开后不含x²,x³,求p、q的值](/uploads/image/z/10755050-50-0.jpg?t=%E8%8B%A5%28x%26%23178%3B%2Bpx%2Bq%29%28x%26%23178%3B-2x-3%29%E5%B1%95%E5%BC%80%E5%90%8E%E4%B8%8D%E5%90%ABx%26%23178%3B%2Cx%26%23179%3B%2C%E6%B1%82p%E3%80%81q%E7%9A%84%E5%80%BC)
若(x²+px+q)(x²-2x-3)展开后不含x²,x³,求p、q的值
若(x²+px+q)(x²-2x-3)展开后不含x²,x³,求p、q的值
若(x²+px+q)(x²-2x-3)展开后不含x²,x³,求p、q的值
展开得:原式=x^4-2x^3-3x^2-px^3-2px^2-3px+qx^2-2qx-3q=x^4+(-3-2p+q)x^2+(-2-p)x^3+……,则因不含x^2与x^3,则-3-2p+q=0且-2-p=0,则p=2,再可推出q=7