一道数学题.英文版的!Given that the equation kx²+12x+k=0,where k is a positive constant ,has equal roots ,find the value of k

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一道数学题.英文版的!Giventhattheequationkx²+12x+k=0,wherekisapositiveconstant,hasequalroots,findthevalue

一道数学题.英文版的!Given that the equation kx²+12x+k=0,where k is a positive constant ,has equal roots ,find the value of k
一道数学题.英文版的!
Given that the equation kx²+12x+k=0,where k is a positive constant ,has equal roots ,find the value of k

一道数学题.英文版的!Given that the equation kx²+12x+k=0,where k is a positive constant ,has equal roots ,find the value of k
方程kx²+12x+k=0,k是正数,有两个相等的根,求k的值
12^2-4k^2=0,k=6(k=-6舍掉)

判别式=0=12^2-4k^2 k=6或-6

b平方减4ac=0时有两个相等的根

12x=2根号k*根号k *x
12=2k
k=6

判别式b²-4ac=0时 式子有两个根

是这个意思,我们知道2次方程式的对称轴是-b/2a,代入该式则为-6/k;
又因为方程式2根相同,说明2次方程与x轴只有一个交点,那么自然可知是对称轴所在的那点就是在x轴上,所以将x=-6/k代入上式,可得36-72+k*k=0;
所以k*k=36;
又因为根是正数,则舍去-6的根,剩余就是答案6。...

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是这个意思,我们知道2次方程式的对称轴是-b/2a,代入该式则为-6/k;
又因为方程式2根相同,说明2次方程与x轴只有一个交点,那么自然可知是对称轴所在的那点就是在x轴上,所以将x=-6/k代入上式,可得36-72+k*k=0;
所以k*k=36;
又因为根是正数,则舍去-6的根,剩余就是答案6。

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