Question

QUESTÃO 69.
Qual deve ser o valor de K na equação x? -
12x + k - 2 = 0, sabendo que uma raiz é o
triplo da outra?​

Answer 1

$\mathsf{x^2-12x+k-2=0}$

$\mathsf{x_{1}=3.x_{2}}\\\mathsf{x_{1}+x_{2}=-\dfrac{b}{a}}\\\mathsf{3x_{2}+x_{2}=-\dfrac{-12}{1}}$

$\mathsf{4x_{2}=12}\\\mathsf{x_{2}=\dfrac{12}{4}}\\\mathsf{x_{2}=3}$

$\mathsf{x_{1}=3.x_{2}}\\\mathsf{x_{1}=3.3=9}$

$\mathsf{x_{1}.x_{2}=\dfrac{c}{a}}\\\mathsf{9.3=\dfrac{k-2}{1}}\\\mathsf{k-2=27}\\\mathsf{k=27+2}$

$\huge\boxed{\boxed{\boxed{\boxed{\mathsf{k=29}}}}}$