if -3 is a root of the equation x^2+(13+k)x+k=0, find
a) the value of k
b) the other root of the equation.
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if -3 is a root of the equation x^2+(13+k)x+k=0...
2007-06-10 11:00 pm
回答 (3)
2007-06-11 12:44 am
✔ 最佳答案
1)x^2+(13+k)x+k=0(-3)^2+-3(13+k)+k=0
-2k=30
k=-15
2)x^2+(13+-(15))x-15=0
x^2-2x-15=0
(x-5)(x+3)=0
x=5
The other root of the equation is 5
參考: me
2007-06-11 11:01 am
Let a be another root of the equation
Sum of roots = a - 3 = -(13+k)
Product of roots = k = -3a
Solving these two equations,
we have a - 3 = -13+3a
which gives a=5
Putting this into k=-3a, we have k = -15
Sum of roots = a - 3 = -(13+k)
Product of roots = k = -3a
Solving these two equations,
we have a - 3 = -13+3a
which gives a=5
Putting this into k=-3a, we have k = -15
2007-06-10 11:12 pm
a)
(-3)^2+(13+k)(-3)+k=0
k=-15
b)
x^2-2x-15=0
x=5 or x=-3
So the other root is x=5
(-3)^2+(13+k)(-3)+k=0
k=-15
b)
x^2-2x-15=0
x=5 or x=-3
So the other root is x=5
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