Question 1164777
<pre>
By this formula:

{{{matrix(1,9,

x^2,
""-"",
(matrix(3,1,SUM,OF,ROOTS))x,
""+"",
(matrix(3,1,PRODUCT,OF,ROOTS)),
"",
""="",
"",
0)}}} 

Put -4 for the sum of roots.

{{{matrix(1,9,

x^2,
""-"",
(-4)x,
""+"",
(matrix(3,1,PRODUCT,OF,ROOTS)),
"",
""="",
"",
0)}}}

One root is given as 7.
Let the other root be R:

Then 7 + R = -4
         R = -4 - 7
         R = -11

Put (7)(-11)=-77 for the product of roots:

{{{matrix(1,9,

x^2,
""-"",
(-4)x,
""+"",
(-77),
"",
""="",
"",
0)}}} 

Simplify the signs:

{{{matrix(1,9,

x^2,
""+"",
4x,
""-"",
77,
"",
""="",
"",
0)}}} 

-------------------------

Check by factoring:

     x² + 4x - 77 = 0
  (x + 11)(x - 7) = 0

x + 11 = 0;   x - 7 = 0
     x = -11;     x = 7     

Edwin</pre>