F4 Maths急!!

2014-01-02 1:15 am

1.The graph y=-3x^2-(8+k)x+k-1 touches the x-axis at point-T
(a) Find the values of k.
(b) If k takes the smaller value, find the coordinates of T.

2.If x^2+2x-3 is multiplied by 1-2x+4x^2-8x^3 and the product is subtracted from -8x^5 , find
(a)The coefficient of x^3
(b)The constant term

求教萬分感激!!!

回答 (1)

用戶4366

2014-01-02 1:38 am

✔ 最佳答案

1.When y = 0; the curve touch x_axis.

that means -3x² -(8+k)x + (k-1) = 0
has double root

(8+k)² - 4(-3)(k-1) = 0 ; ∆ = b² - 4ac = 0

k² + 16k + 64 +12(k-1) = 0

k² + 28k + 52 = 0

(k+26)(k+2) = 0

k = -26 or k = -2

when k = -26

x = -[-(8-26)]/[2(-3)] = 3

touching point ( 3,0 )

2014-01-01 17:53:32 補充：
(1-2x+4x²-8x³)(x²+2x-3)

=x²-2x³+4x⁴-8x⁵+2x-4x²+8x³-16x⁴-3+6x-12x²+24x³

=-8x⁵-12x⁴+30x³-15x²+8x-3

-8x⁵ - ( -8x⁵-12x⁴+30x³-15x²+8x-3 )

= 12x⁴-30x³+15x²-8x+3

The coefficient of x³ = -30

The constant term = 3

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