八上数学无解题目及答案

八上数学无解题目及答案一、选择题（每题3分，共30分）1.若方程\(x^2+3x+2=0\)无解，则下列哪个选项是正确的？A.\(\Delta=9-8=1>0\)B.\(\Delta=9-8=1<0\)C.\(\Delta=9-8=1=0\)D.\(\Delta=9-8=1\)无法确定答案：B2.对于方程\(x^2-4x+4=0\)，下列哪个选项描述了方程的解？A.无解B.有两个不同的实数解C.有两个相同的实数解D.有一个实数解答案：C3.方程\(x^2-6x+9=0\)的判别式\(\Delta\)是多少？A.\(\Delta=36-36=0\)B.\(\Delta=36-36=1\)C.\(\Delta=36-36=-1\)D.\(\Delta=36-36=36\)答案：A4.若方程\(x^2+2x+1=0\)无解，下列哪个选项是正确的？A.\(\Delta=4-4=0\)B.\(\Delta=4-4=1\)C.\(\Delta=4-4=-1\)D.\(\Delta=4-4=4\)答案：C5.方程\(x^2+5x+6=0\)的判别式\(\Delta\)是多少？A.\(\Delta=25-24=1\)B.\(\Delta=25-24=-1\)C.\(\Delta=25-24=0\)D.\(\Delta=25-24=25\)答案：A6.若方程\(x^2-2x+1=0\)无解，下列哪个选项是正确的？A.\(\Delta=4-4=0\)B.\(\Delta=4-4=1\)C.\(\Delta=4-4=-1\)D.\(\Delta=4-4=4\)答案：C7.方程\(x^2-8x+16=0\)的判别式\(\Delta\)是多少？A.\(\Delta=64-64=0\)B.\(\Delta=64-64=1\)C.\(\Delta=64-64=-1\)D.\(\Delta=64-64=64\)答案：A8.若方程\(x^2+7x+12=0\)无解，下列哪个选项是正确的？A.\(\Delta=49-48=1\)B.\(\Delta=49-48=-1\)C.\(\Delta=49-48=0\)D.\(\Delta=49-48=49\)答案：B9.方程\(x^2-10x+25=0\)的判别式\(\Delta\)是多少？A.\(\Delta=100-100=0\)B.\(\Delta=100-100=1\)C.\(\Delta=100-100=-1\)D.\(\Delta=100-100=100\)答案：A10.若方程\(x^2-3x+2=0\)无解，下列哪个选项是正确的？A.\(\Delta=9-8=1\)B.\(\Delta=9-8=-1\)C.\(\Delta=9-8=0\)D.\(\Delta=9-8=9\)答案：B二、填空题（每题2分，共20分）1.方程\(x^2+4x+4=0\)的判别式\(\Delta\)为\(\Delta=16-16=\boxed{0}\)。2.方程\(x^2-6x+9=0\)的判别式\(\Delta\)为\(\Delta=36-36=\boxed{0}\)。3.方程\(x^2+2x+1=0\)的判别式\(\Delta\)为\(\Delta=4-4=\boxed{0}\)。4.方程\(x^2-4x+4=0\)的判别式\(\Delta\)为\(\Delta=16-16=\boxed{0}\)。5.方程\(x^2+6x+9=0\)的判别式\(\Delta\)为\(\Delta=36-36=\boxed{0}\)。6.方程\(x^2-2x+1=0\)的判别式\(\Delta\)为\(\Delta=4-4=\boxed{0}\)。7.方程\(x^2-8x+16=0\)的判别式\(\Delta\)为\(\Delta=64-64=\boxed{0}\)。8.方程\(x^2+5x+6=0\)的判别式\(\Delta\)为\(\Delta=25-24=\boxed{1}\)。9.方程\(x^2-10x+25=0\)的判别式\(\Delta\)为\(\Delta=100-100=\boxed{0}\)。10.方程\(x^2-3x+2=0\)的判别式\(\Delta\)为\(\Delta=9-8=\boxed{1}\)。三、解答题（每题10分，共50分）1.解方程\(x^2+3x+2=0\)并说明是否有解。解：方程的判别式\(\Delta=3^2-4\cdot1\cdot2=9-8=1\)。因为\(\Delta>0\)，所以方程有两个不同的实数解。解得\(x=\frac{-3\pm\sqrt{1}}{2}=\frac{-3\pm1}{2}\)，即\(x_1=-1\)，\(x_2=-2\)。因此，该方程有解。2.解方程\(x^2-4x+4=0\)并说明是否有解。解：方程的判别式\(\Delta=(-4)^2-4\cdot1\cdot4=16-16=0\)。因为\(\Delta=0\)，所以方程有两个相同的实数解。解得\(x=\frac{4\pm\sqrt{0}}{2}=2\)。因此，该方程有解。3.解方程\(x^2-6x+9=0\)并说明是否有解。解：方程的判别式\(\Delta=(-6)^2-4\cdot1\cdot9=36-36=0\)。因为\(\Delta=0\)，所以方程有两个相同的实数解。解得\(x=\frac{6\pm\sqrt{0}}{2}=3\)。因此，该方程有解。4.解方程\(x^2+2x+1=0\)并说明是否有解。解：方程的判别式\(\Delta=2^2-4\cdot1\cdot1=4-4=0\)。因为\(\Delta=0\)，所以方程有两个相同的实数解。解得\(x=\frac{-2\pm\sqrt{0}}{2}=-1\)。因此，该方程有解。5.解方程\(x^2-2x+1=0\)并说明是否有解。