Question

Решите с объяснением пожалуйста! Даю 40 бал, Теорема Виэта!

10x^2+kx-7=0, x1=-1/5, x2=?, k=?

Answer 1

$\displaystyle\bf\\10x^{2} +kx-7=0\\\\Teorema \ Vieta:\\\\x_{1} \cdot x_{2} =-\frac{7}{10} =-0,7\\\\x_{1} =-\frac{1}{5} \\\\x_{2} =-0,7:x_{1} =-0,7:\Big(-\frac{1}{5} )=-0,7\cdot(-5)=3,5\\\\\boxed{\boxed{x_{2} =3,5}}\\\\\\Teorema \ Vieta:\\\\x_{1} +x_{2} =-\frac{k}{10} \\\\-\frac{k}{10} =-\frac{1}{5} +3,5=-0,2+3,5=3,3\\\\-\frac{k}{10}=3,3\\\\-k=33\\\\\boxed{\boxed{k=-33}}$