Some different kinds of questions?
Factorize 2a^(n+1)-7a^n-30a^(n-1)
find the range of values of k that equation x^2+(k -2)x+1=0 has real roots
Simultaneous equation y=x^2-7x+2,y=x-(5k+4) have only one set of real solution and k is constant.find k
1.Factorize 2a^(n+1)-7a^n-30a^(n-1)
find the range of values of k that equation x^2+(k -2)x+1=0 has real roots
Simultaneous equation y=x^2-7x+2,y=x-(5k+4) have only one set of real solution and k is constant.find k

1 個解答
- YA HOO!知識+管理員Lv 65 年前最愛解答
Factorize 2a^(n+1)-7a^n-30a^(n-1)
2aⁿ⁺¹ - 7aⁿ - 30aⁿ⁻¹
= (2a²) aⁿ⁻¹ - (7a) aⁿ⁻¹ - 30 aⁿ⁻¹
= aⁿ⁻¹ (2a² - 7a - 30)
x² + (k - 2) x + 1 = 0
∵ The equation has real roots
∴ Δ ≥ 0
(k - 2)² - 4 (1) (1) ≥ 0
k² - 4k + 4 - 4 ≥ 0
k (k - 4) ≥ 0
k ≤ 0 or k ≥ 0
y = x² - 7x + 2 y = x - (5k + 4)
x² - 7x + 2 = x - (5k + 4)
x² - 7x + 2 - x + (5k + 4) = 0
x² - 8x + (5k + 6) = 0
∵ The equations have one set of real solution
∴ Δ = 0
(-8)² - 4 (1) (5k + 6) = 0
64 - 20k - 24 = 0
20k = 40
k = 2
7.
Since ABCD is a rectangle,
BE = DE
x + 6 = 3x - 2
3x - x = 6 + 2
2x = 8
x = 4
∴ D. 4