Question

Составьте квадратные уравнения с корнями​

Answer 1

$\boxed {\; x^2+px+q=(x-x_1)(x-x_2)\; }\\\\\\1)\; \; x_1=x_2=\frac{4}{9}\\\\(x-\frac{4}{9})(x-\frac{4}{9})=(x-\frac{4}{9})^2=x^2-\frac{8}{9}\, x+\frac{16}{81}=0\\\\81x^2-72x+16=0\\\\\\2)\; \; x_1=x_2=-3\frac{1}{4}=-\frac{13}{4}\\\\(x+\frac{13}{4})^2=x^2+\frac{13}{2}\, x+\frac{169}{4}=0\\\\4x^2+26x+169=0$

$3)\; \; x_1=5\frac{4}{7}=\frac{39}{7}\; \; ,\; \; x_2=-5\frac{4}{7}=-\frac{39}{7}\\\\(x-\frac{39}{7})(x+\frac{39}{7})=0\\\\x^2-(\frac{39}{7})^2=0\\\\x^2- \frac{1521}{49}=0\\\\49x^2-1521=0$

$4)\; \; x_1=-\sqrt7\; ,\; \; x_2=\sqrt7\\\\(x-\sqrt7)(x+\sqrt7)=x^2-7\\\\x^2-7=0$