Question

помогите срочно надо ​

Answer 1

Ответ:

$1)\ \ x_1=3\ ,\ \ x_2=5\\\\\\x^2+px+q=0\ \ \ \Rightarrow \ \ \ \left\{\begin{array}{l}x_1+x_2=-p\\x_1\cdot x_2=q\end{array}\right\ \ \left\{\begin{array}{l}3+5=-p\\3\cdot 5=q\end{array}\right\ \ \left\{\begin{array}{l}p=-8\\q=15\end{array}\right\\\\\\\boxed{x^2-8x+15=0}$

$2)\ \ x_1=-\dfrac{7}{12}\ \ ,\ \ x_2=\dfrac{3}{2}\ \ \ \left\{\begin{array}{l}-\dfrac{7}{12}+\dfrac{3}{2}=-p\\\\-\dfrac{7}{12}\cdot \dfrac{3}{2}=q\end{array}\right\ \ \left\{\begin{array}{l}-p=\dfrac{-7+18}{12}=\dfrac{11}{12}\\q=-\dfrac{21}{24}\end{array}\right\\\\\\x^2-\dfrac{11}{12}\, x-\dfrac{21}{24}=0\ \Big|\cdot 24\ \ \ \ \ \Rightarrow \ \ \ \boxed{\ 24x^2-11x-21=0\ }$