已知二次函数f(x)=x^2+px+q,且方程f(x)=0与f(2x)=0有相同的非零实根.（1）求q/p^2的值；（2）若f(1)=28,解方程f(x)=0

已知二次函数f(x)=x^2+px+q,且方程f(x)=0与f(2x)=0有相同的非零实根.（1）求q/p^2的值；（2）若f(1)=28,解方程f(x)=0
已知二次函数f(x)=x^2+px+q,且方程f(x)=0与f(2x)=0有相同的非零实根.
（1）求q/p^2的值；
（2）若f(1)=28,解方程f(x)=0

已知二次函数f(x)=x^2+px+q,且方程f(x)=0与f(2x)=0有相同的非零实根.（1）求q/p^2的值；（2）若f(1)=28,解方程f(x)=0
1）
f（x）=0即：x²+px+q=0.1
f（2x）=0即：（2x）²+p（2x）+q=0.2
1式×4 -2式得：2px+3q=0,x=-3q/2p
2式- 1式×2得：2x²-q=0,x²=q/2
∴q/2=（-3q/2p）²
q/p²=2/9
2）
f（1）=28,即：1+p+q=28
p+q=27
又q/p²=2/9
联立两方程求p=9,q=18,或p=-27/2,q=81/2
当p=9,q=18时,f（x）=x²+9x+18
f（x）=0即：x²+9x+18=0
x1=-3,x2=-6
当p=-27/2,q=81/2时,f（x）=x²-27x/2 +81/2
f（x）=0即：x²-27x/2 +81/2=0
x1=9/2,x2=9

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good crisp blue piercing brightly color
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