(急!)如果一元二次方程ax²+bx+c=0(a不等于0)有两个实数根x1和x2,请用含有a,b,c的代数式表示:(1)x1+x2 (2)x1乘x2
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![(急!)如果一元二次方程ax²+bx+c=0(a不等于0)有两个实数根x1和x2,请用含有a,b,c的代数式表示:(1)x1+x2 (2)x1乘x2](/uploads/image/z/325684-28-4.jpg?t=%28%E6%80%A5%21%EF%BC%89%E5%A6%82%E6%9E%9C%E4%B8%80%E5%85%83%E4%BA%8C%E6%AC%A1%E6%96%B9%E7%A8%8Bax%26%23178%3B%2Bbx%2Bc%3D0%28a%E4%B8%8D%E7%AD%89%E4%BA%8E0%29%E6%9C%89%E4%B8%A4%E4%B8%AA%E5%AE%9E%E6%95%B0%E6%A0%B9x1%E5%92%8Cx2%2C%E8%AF%B7%E7%94%A8%E5%90%AB%E6%9C%89a%2Cb%2Cc%E7%9A%84%E4%BB%A3%E6%95%B0%E5%BC%8F%E8%A1%A8%E7%A4%BA%EF%BC%9A%EF%BC%881%EF%BC%89x1%2Bx2+%282%29x1%E4%B9%98x2)
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(急!)如果一元二次方程ax²+bx+c=0(a不等于0)有两个实数根x1和x2,请用含有a,b,c的代数式表示:(1)x1+x2 (2)x1乘x2
(急!)如果一元二次方程ax²+bx+c=0(a不等于0)
有两个实数根x1和x2,请用含有a,b,c的代数式表示:(1)x1+x2 (2)x1乘x2
(急!)如果一元二次方程ax²+bx+c=0(a不等于0)有两个实数根x1和x2,请用含有a,b,c的代数式表示:(1)x1+x2 (2)x1乘x2
x1=[-b-√(b²-4ac)]/2a
x2=[-b+√(b²-4ac)]/2a
所以
x1+x2=[-b-√(b²-4ac)]/2a+[-b+√(b²-4ac)]/2a
=[-b-√(b²-4ac)-b+√(b²-4ac)]/2a
=-2b/2a
=-b/a
x1x2=[-b-√(b²-4ac)][-b+√(b²-4ac)]/4a²
分子是平方差
=(b²-b²+4ac)/4a²
=4ac/4a²
=c/a
x1+x2=-(b/a)
x1*x2=c/a
(1)x1+x2=-b/a (2)x1乘x2=c/a