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Given that a is the root of each of the equations xsquare-5x plus k equals 0 and xsquare-6x plus 3k equals 0 where k is not equal to 0 find k and a?
Wiki User
∙ 14y ago
Since a is the root of both equations, a satisfies them:
a2 - 5a + k = 0
a2 - 6a + 3k = 0
The right hand side of both the equations are same. Therefore,
a2 - 5a + k = a2 - 6a + 3k
6a - 5a = 3k - k
a = 2k
k = (a/2)
Substituting k = a/2 in one of the equations,
a2 - 5a + (a/2) = 0
Solving, a=9/2
k=a/2=9/4
Thus 'a' = (9/2) and 'k' = (9/4).
Wiki User
∙ 14y ago
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