Math Help - quadratic equation

three points : A=3,2 B=1,2 C=0,k with k being a constant

AC=5BC

FIND THE VALUES OF K

my teacher said to use a quadratic please help

Originally Posted by kitobeirens

three points : A=3,2 B=1,2 C=0,k with k being a constant
AC=5BC
FIND THE VALUES OF K
my teacher said to use a quadratic please help

Solve

Originally Posted by Plato

......

The 25 should be 5.
You'll get 2 valid solutions.

Originally Posted by Wilmer

The 25 should be 5.
You'll get 2 valid solutions.

Think again:

My bad. Jumped on "5" and got nice integer solutions: k=1 or k=3;
both "looked" good on my quickly sketched diagram!

BUT: if the correct "25" is used, then : k = [6 +- sqrt(-6)] / 3;
so no real solution.
Perhaps the OP made a typo....

Originally Posted by Wilmer

My bad. Jumped on "5" and got nice integer solutions: k=1 or k=3;
both "looked" good on my quickly sketched diagram
BUT: if the correct "25" is used, then : k = [6 +- sqrt(-6)] / 3;
so no real solution.
Perhaps the OP made a typo....

I suspect that whoever wrote the question made the mistake.
The 5 does give a very nice solution. So it should have been .