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.

Update:

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?

Update 2:

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

Update 3:

Hence, I can just only solve the quadratic equation by factor method, quadratic formula, graphical method

Update 4:

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

Rating
  • 1 decade ago
    Favorite 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
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