作业帮一道AMC数学题The real number c,b,a form an arithmetic sequence wi
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一道AMC数学题
The real number c,b,a form an arithmetic sequence with a≥b≥c≥0.The quadratic ax²+bx+c has exactly one root.What is this root?
(A) -7-4√3(B) -2-√3(C) -1(D) -2+√3(E)-7+4√3
The real number c,b,a form an arithmetic sequence with a≥b≥c≥0.The quadratic ax²+bx+c has exactly one root.What is this root?
(A) -7-4√3(B) -2-√3(C) -1(D) -2+√3(E)-7+4√3
公差为根号3/2
∴根为：-2+根号3
选D
再问： 不太懂，公差？
再答： arithmetic sequence 的意思为等差数列
再问： 怎么求的公差，大神帮帮我
再答： ax²+bx+c=0 设公差为d b=a+d，c=a-d ∵b^2-4ac=0 ∴b^2-4(b+d)(b-d)=0 ∴4d^2-3b^2=0 ∴d=根号3/2b 不好意思之前漏了b。 然后x=-b/2a就能算了
∴根为：-2+根号3
选D
再问： 不太懂，公差？
再答： arithmetic sequence 的意思为等差数列
再问： 怎么求的公差，大神帮帮我
再答： ax²+bx+c=0 设公差为d b=a+d，c=a-d ∵b^2-4ac=0 ∴b^2-4(b+d)(b-d)=0 ∴4d^2-3b^2=0 ∴d=根号3/2b 不好意思之前漏了b。 然后x=-b/2a就能算了
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