f(x)=2x^2-4x-1 eching

$$f ( x ) = 2 x ^ { 2 } - 4 x - 1$$

Omil

$$2\left(x-\left(-\frac{\sqrt{6}}{2}+1\right)\right)\left(x-\left(\frac{\sqrt{6}}{2}+1\right)\right)$$

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.

$$2x^{2}-4x-1=0$$

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.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 2\left(-1\right)}}{2\times 2}$$

-4 kvadratini chiqarish.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\times 2\left(-1\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16-8\left(-1\right)}}{2\times 2}$$

-8 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16+8}}{2\times 2}$$

16 ni 8 ga qo'shish.

$$x=\frac{-\left(-4\right)±\sqrt{24}}{2\times 2}$$

24 ning kvadrat ildizini chiqarish.

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

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±2\sqrt{6}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{4±2\sqrt{6}}{4}$$

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

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

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

$$x=\frac{\sqrt{6}}{2}+1$$

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

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

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

$$x=-\frac{\sqrt{6}}{2}+1$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 1+\frac{\sqrt{6}}{2} ga va x_{2} uchun 1-\frac{\sqrt{6}}{2} ga bo‘ling.

$$2x^{2}-4x-1=2\left(x-\left(\frac{\sqrt{6}}{2}+1\right)\right)\left(x-\left(-\frac{\sqrt{6}}{2}+1\right)\right)$$

Baholash

$$2x^{2}-4x-1$$