Question 310917
If one solution to the equation x^2 – 3x + k = 0 is 4, then what is the other solution? 
a) -4 b) -1 c) 1 
d) 4 e) cannot be determined from the information given 
<pre><font size = 4 color = "indigo"><b>
 x<sup>2</sup> – 3x + k = 0

Since 4 is a solution, it must satisfy that equation when
4 is substituted for x.  Substituting 4 for x in

 x<sup>2</sup> – 3x + k = 0

gives

(4)<sup>2</sup> – 3(4) + k = 0

  16 - 3(4) + k = 0

    16 - 12 + k = 0
  
          4 + k = 0

              k = -4

Substituting -4 for k in

   x<sup>2</sup> – 3x + k = 0

gives

    x<sup>2</sup> – 3x + (-4) = 0

       x<sup>2</sup> – 3x - 4 = 0

    (x - 4)(x + 1) = 0

    x - 4 = 0,   x + 1 = 0
        x = 4,       x = -1

So the other solution is -1, choice b)

Edwin</pre>