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【简答题】
已知函数f（x）=ax 2 +bx+1（a，b为实数），x∈R，F（x）= f(x)(x＞0) -f(x)(x＜0) （1）若f（-1）=0且函数f（x）的值域为[0，+∞），求F（x）的表达式； （2）设mn＜0，m+n＞0，a＞0，且f（x）为偶函数，判断F（m）+F（n）能否大于零？并说明理由．
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