F.4 Quadratic Equation
1. It is given that k is a root of the quadratic equation x^2 + x + c = 0.
(a) Express c in terms of k.
x^2 + x + c = 0
k^2 + k + c = 0
c = -k^2 - k
(b) Find the other root of the equation in (a).
How to do so? And explain the steps clearly. Thanks a lot.
root one +root two = - b/a
root one x root two = c/a
I just find this two principles to solve this equation
they are related to product of roots and sum of roots
They are Chapter 2 in my maths book but the question is in Chapter 1
Hence, I can just only solve the quadratic equation by factor method, quadratic formula, graphical method
For the curve x^2 + x + c = 0
By using Quadratic formula,
- 1 ± √[1-4(1)(c)] / 2(1)
=- 1 ± √[1-4(-k^2 - k) / 2
=- 1 ± √(1+4k^2 +4k) / 2
=- 1 ± √(2k+1)^2 / 2
=- 1 + (2k+1) / 2 or - 1 - (2k+1) / 2
= k or -k - 1
The other root is - k - 1
- Prof. PhysicsLv 71 decade agoFavorite Answer
In part a, you find out that c = -k2 - k
b. Let the other root be m.
The equation is: x2 + x - (k2 + k) = 0
We consider the sum of roots, m + k = -1
Therefore, m = -k - 1
Or we may consider the product of roots, mk = -(k2 + k)
m = -k - 1
2009-09-23 20:45:01 補充：
I realize that it is a g.math question.
So, I would rather use another method.
Let m be the other root.
So, the equation can be expressed as (x - k)(x - m) = 0
x^2 - (k + m)x + km = 0
So, using the same method as I used.Source(s): Physics king