Question

3° ANO

Os valores de x que tornam os pontos L ( 2, 1 ). M ( -4, x ) e N ( x, 0 ) colineares são:​

Answer 1

$\Large\boxed{\begin{array}{l}\sf os~pontos~ser\tilde ao~colineares~quando\\\sf\begin{vmatrix}\sf2&\sf1&\sf1\\\sf-4&\sf x&\sf1\\\sf x&\sf0&\sf1\end{vmatrix}=0\\\sf 2\cdot(x-0)-1\cdot(-4-x)+1\cdot(0-x^2)=0\\\sf 2x+4+x-x^2=0\\\sf -x^2+3x+4=0\cdot(-1)\\\sf \end{array}}$

$\Large\boxed{\begin{array}{l}\sf x^2-3x-4=0\\\sf\Delta=b^2-4ac\\\sf\Delta=(-3)^2-4\cdot1\cdot(-4)\\\sf\Delta=9+16\\\sf\Delta=25\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\sf x=\dfrac{-(-3)\pm\sqrt{25}}{2\cdot1}\\\\\sf x=\dfrac{3\pm5}{2}\begin{cases}\sf x_1=\dfrac{3+5}{2}=\dfrac{8}{2}=4\\\\\sf x_2=\dfrac{3-5}{2}=-\dfrac{2}{2}=-1\end{cases}\end{array}}$