Question

Quais são os possíveis valores de c para que os pontos (c, 3), (2, c) e (14, -3) sejam colineares?

Answer 1

$\huge\begin{vmatrix}c&3&1\\2&c&1\\14&-3&1\end{vmatrix}=0$

$\mathsf{c(c+3)-3(2-14)+1(-6-14c)=0}\\\mathsf{c^2+3c+36-6-14c=0}\\\mathsf{c^2-11c+30=0}$

$\mathsf{\Delta=121-120=1}\\\mathsf{c=\dfrac{11\pm1}{2}\begin{cases}c_{1}=6\\c_{2}=5\end{cases}}$