8. If the product of the roots of the quadratic equation(k+1)x^2 - 10x + k -1=0 is 2 ,where k ≠ -1
a)find the value of k
b)the sum of the roots.
10.If one root of x^2-6x+k=0 is 2, find the other root and the value of k.
11.If α and β are the roots of the equation x^2+x-9+0,find the value of
a)α + β
b)αβ
c)(a+1)(β+1)
d)α ^2+ β^2
12.If α and β are the roots of the equation x^2+2x-6=0,find the values of
a) 1⊥α + 1⊥β ⊥←分線
b)a^2β+aβ^2
c)(a-2)(β-2)
d)a^2+2β作者: 富商.豪 時間: 09-9-21 08:36 PM
8a) (k-1)/(k+1) = 2
k-1 = 2k+2
k = -3
8b) sum of roots : -(-10/(k+1)) = 10/(-3+1) = -5
10)since root of eqt is 2,
so, 2^2 -6(2) + k = 0
k = 8
eqt: x^2 -6x +8 = 0
(x-4)(x-2) = 0
x = 4 or 2
so the other root is 4.
11.. 應該是x^2 + x - 9=0吧..!? 你打了+0
11a)-1 11b) -9
11c) i assume that α = a and β = b
(a+1)(b+1)
= ab +( a + b )+ 1
= -9 -1 +1
= -9
11d) a^2+b^2
= a^2+2ab+b^2 - 2ab
= (a+b)^2 - 2ab
= (-1)^2 - 2(-9)
= 1+18 = 19