If 11x^2-2x+2=k(1-4x+2x^2) has two equal real roots, find the values of k.
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中四數學問題Quadratic equation
2010-09-11 6:22 am
回答 (2)
2010-09-11 6:38 am
✔ 最佳答案
11x^2-2x+2=k(1-4x+2x^2)11x^2-2x+2=k-4kx+2kx^2
(11-2k)x^2+(4k-2)x+(2-k)=0...(*)
Since the equation has two equal real roots, then the discriminant of (*)=0
(4k-2)^2-4(11-2k)(2-k)=0
16k^2-16k+4-4(22-15k+2k^2)=0
8k^2+44k-84=0
k=3/2 or k=-7
2010-09-11 6:51 am
11x^2-2x+2=k(1-4x+2x^2)
11x^2-2x+2=k-4kx+2kx^2
11x^2-2x+2-k+4kx-2kx^2=0
(11-2k)x^2+(4k-2)x+(2-k)=0
11x^2-2x+2=k(1-4x+2x^2) has two equal real roots
⊿=0
(4k-2)^2- 4(11-2k)(2-k)=0
16k^2-16k+4- 8k^2+60k- 88=0
8k^2+44k- 84=0
(2x-3)(x+7)=0
x=3/2 or -7
11x^2-2x+2=k-4kx+2kx^2
11x^2-2x+2-k+4kx-2kx^2=0
(11-2k)x^2+(4k-2)x+(2-k)=0
11x^2-2x+2=k(1-4x+2x^2) has two equal real roots
⊿=0
(4k-2)^2- 4(11-2k)(2-k)=0
16k^2-16k+4- 8k^2+60k- 88=0
8k^2+44k- 84=0
(2x-3)(x+7)=0
x=3/2 or -7
參考: me
收錄日期: 2021-04-19 23:12:23
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