Re: [中學] 二次函數一題
: 請問這題該怎麼著手呢?
: 謝謝~
設f(x) = ax^2+bx+c
f(0) = -3 = c
f(1) = -4 = a+b-3 => a+b = -1
令f(x) = ax^2+bx-3 = 0 的兩根為 α、β
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|α-β| = √b^2+12a / |a| = 4
=> b^2+12a = 16a^2 (以b =-a-1代入)
=> a^2-2a+1+12a = 16a^2
=> 15a^2-14a-1 = 0
=> a = -1/15 or 1
欲求 f(-1) = a-b-3 = 2a-2 = -32/15 or 0 #
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