Form a quadratic equation in x with given roots for each of the following: 1) 5, 1/2, 2) 2/3, -4/5, 3) -2’1/2, -1’3/4.

Question

explanation and working out please.

(just letting you know that “-2’1/2“ is 2 whole, 1 over 2 in a fraction.)

Answer 1

It would be best for you just to given the roots as improper fractions, e.g -7/4.

 

The way to do this is simply to form f(x) = (x-root)(x-other root), in general.

 

So for # 1, a quadratic that has those roots is f(x) = (x-5)(x-½) = 0.

 

In case you want no fractions, then multiply f(x) by the LCD, i.e. the second factor above could be (2x-1).

Then you FOIL to put the function into standard form

Answer 2

1)

 

   x = 5  and x = 1/2

 

   (x-5)=0  and (2x - 1) = 0

 

   (x-5)(2x-1) = 0

 

  FOIL method left for you

 

 

2)       x = 2/3 and x = -4/5

 

         (3x - 2)(5x +4) = 0

 

 

3)   x = - 2 and 1/2    AND  x = -1 and 3/4

 

      x = - 5/2   and   x= -7/4

 

    (2x+5)(4x+7) = 0