f(x)=x^2-6x-19 eching

$$f ( x ) = x ^ { 2 } - 6 x - 19$$

Omil

$$\left(x-\left(3-2\sqrt{7}\right)\right)\left(x-\left(2\sqrt{7}+3\right)\right)$$

Kvadrat tenglamalaridan foydalanish qoidalari

Kvadrat koʻp tenglama bu orqali hisoblanadi: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), bu yerda x_{1} va x_{2} ax^{2}+bx+c=0 kvadrat tenglamaning yechimlari.

$$x^{2}-6x-19=0$$

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni kvadrat formulasi bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat formula ikki yechmni taqdim qiladi, biri ± qo'shish bo'lganda, va ikkinchisi ayiruv bo'lganda.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-19\right)}}{2}$$

-6 kvadratini chiqarish.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-19\right)}}{2}$$

-4 ni -19 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36+76}}{2}$$

36 ni 76 ga qo'shish.

$$x=\frac{-\left(-6\right)±\sqrt{112}}{2}$$

112 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±4\sqrt{7}}{2}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±4\sqrt{7}}{2}$$

x=\frac{6±4\sqrt{7}}{2} tenglamasini yeching, bunda ± musbat. 6 ni 4\sqrt{7} ga qo'shish.

$$x=\frac{4\sqrt{7}+6}{2}$$

6+4\sqrt{7} ni 2 ga bo'lish.

$$x=2\sqrt{7}+3$$

x=\frac{6±4\sqrt{7}}{2} tenglamasini yeching, bunda ± manfiy. 6 dan 4\sqrt{7} ni ayirish.

$$x=\frac{6-4\sqrt{7}}{2}$$

6-4\sqrt{7} ni 2 ga bo'lish.

$$x=3-2\sqrt{7}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 3+2\sqrt{7} ga va x_{2} uchun 3-2\sqrt{7} ga bo‘ling.

$$x^{2}-6x-19=\left(x-\left(2\sqrt{7}+3\right)\right)\left(x-\left(3-2\sqrt{7}\right)\right)$$

Baholash

$$x^{2}-6x-19$$