F.4 a.maths [復制鏈接]

If the equations x^2-4x+k=0 and 2x^2-3x+k=0 have a common root α,find the value of k.

k=-5 or 0

thx

下面是引用yukyty於2006-01-08 19:42發表的F.4 a.maths:
If the equations x^2-4x+k=0 and 2x^2-3x+k=0 have a common root α,find the value of k.
k=-5 or 0
thx

tht's the answer?

下面是引用望晴天於2006-01-08 19:49發表的:
tht's the answer?

yes,i want the step

x^2-4x+k = 2x^2-3x+k
x^2+x = 0
x(x+1) = 0
x=0 or x=-1

Case-I (x=0):

subs x=0 into the 1st equation:
0-0+k=0
k=0

Case-II (x=-1)

subs x=-1 into the 1st equatio:
1-4(-1)+k=0
5+k=0
k=-5

why x^2-4x+k = 2x^2-3x+k?

下面是引用yukyty於2006-01-08 20:05發表的:
why x^2-4x+k = 2x^2-3x+k?

they possess common root

If the maximum value of f(x)=2kx^2-12x-k,where k<0,is 11,find the value of k.

k=-9 or -2

2kx^2 - 12x - k
= 2k [ x^2 - (6/k) x - 1/2 ]
= 2k [ x^2 - (6/k) x + (6/2k)^2 - 1/2 - (6/2k)^2 ]
= 2k (x-3/k)^2 + 2k (-1/2 - 9/k^2)

2k (-1/2 - 9/k^2) = 11
11k = -k^2 - 18
k^2 + 11k + 18 = 0
k=-2 or k=-9