1.the figure showa the graph of y=-x^2+6x+k.it cuts the x-axis at two points A and B,and passes through the pointC(-1,9)
(A)find the value of k.
(B)find the coordinates of a and b.
2.in each of the following,form a quadratic equation in x with the given roots,and write the equation in the general form.
(A)2over-5,1over5
(B)1over3,1over3
3.form a quadratic equation in x whose roots are the reciprocals of the roots of(5x+2)(x-4)=0,and write the equation in the general form.
f.4一元二次方程(I)(10分)
2014-09-24 4:13 am
回答 (2)
2014-09-24 7:44 am
✔ 最佳答案
1.(a)
Put x = -1 and y = 9 into the equation y = -x² +6x + k :
9 = -(-1)² + 6(-1) + k
k = 16
(b)
The graph : y = -x² + 6x + 16 ...... [1]
x-axis : y = 0 ...... [2]
[1] = [2] :
-x² + 6x + 16 = 0
x² - 6x - 16 = 0
(x + 2)(x - 8) = 0
x = -2 or x = 8
The coordinates of A and B are (-2,0) and (8, 0) respectively.
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2.
(A)
x = 2/(-5) or x = 1/5
[x + (2/5)] [x - (1/5)] = 0
(5x + 2)(5x - 1) = 0
25x² + 5x - 2 = 0
(B)
x = 1/3 or x = 1/3
[x - (1/3)]² = 0
(3x - 1)² = 0
9x² - 6x + 1 = 0
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3.
-2/5 and 4 are the roots of (5x + 2)(x - 4) = 0
Then -5/2 and 1/4 are the roots of the required quadratic equation.
[x + (5/2)] [x - (1/4)] = 0
(2x + 5)(4x - 1) = 0
8x² + 18x - 5 = 0
參考: 土扁
2014-09-24 4:24 am
為了清楚表達，a over b 可以打作 a/b，意指 a ÷ b。
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