F.4 A maths一問

Since B is the common root of x²-4x+k=0 and 2x²-3x+k=0
B²-4B+k=0---(1)
2B²-3B+k=0---(2)
From (1): -k=B²-4B---(3)
From (2): -k=2B²-3B---(4)
Therefore B²-4B=2B²-3B
B²+B=0
B(B+1)=0
B=0 or B=-1
Sub B=0 into (3):
-k=(0)²-4(0)=0
Therefore k=0
Sub B=-1 into (3):
-k=(-1)²-4(-1)=5
Therefore k=5
Therefore k=-5 or k=0

Let x2﹣4x+k=0..........(1 )
2x2﹣3x+k=0.........(2)

Subsititute x = a into both equations,
we have:
a2﹣4a = 2a2﹣3a
a2 + a = 0
a = 0 or a = -1

put x = 0 into (1) and (2),
k = 0

put x = -1 into (1),
1 + 4 + k = 0
k = -5

Therefore,the value of k is -5 or 0