9/11/2014
One
root of the equation x2
+ kx
+ 8 = 0 is twice the other. Find the roots and all possible values of
k.
Scroll down for the solution.
9/11/2014
Solution.
If
r
and 2r
are
two the roots, since the sum of the roots of a quadratic function is
-b/a,
for
x2
+ kx
+ 8 = 0 → Sum = 3r
= -k/1
= -k
so that r
= -k/3
→ k
= -3r.
Also,
the product of the roots is c/a,
for x2
+ kx
+ 8 = 0 → Product = 2r2
= 8 so that r
= ±2.
Therefore, the roots are 2 and 4 or
-2 and -4, and k
= -3r
=
±6.