# 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.

Solution:

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

How come?

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

Sol:

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

### 1 Answer

- 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