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

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

Omil

$$2\left(x-\frac{-\sqrt{3}-1}{2}\right)\left(x-\frac{\sqrt{3}-1}{2}\right)$$

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.

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

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.

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

2 kvadratini chiqarish.

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

-4 ni 2 marotabaga ko'paytirish.

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

-8 ni -1 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4+8}}{2\times 2}$$

4 ni 8 ga qo'shish.

$$x=\frac{-2±\sqrt{12}}{2\times 2}$$

12 ning kvadrat ildizini chiqarish.

$$x=\frac{-2±2\sqrt{3}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{-2±2\sqrt{3}}{4}$$

x=\frac{-2±2\sqrt{3}}{4} tenglamasini yeching, bunda ± musbat. -2 ni 2\sqrt{3} ga qo'shish.

$$x=\frac{2\sqrt{3}-2}{4}$$

-2+2\sqrt{3} ni 4 ga bo'lish.

$$x=\frac{\sqrt{3}-1}{2}$$

x=\frac{-2±2\sqrt{3}}{4} tenglamasini yeching, bunda ± manfiy. -2 dan 2\sqrt{3} ni ayirish.

$$x=\frac{-2\sqrt{3}-2}{4}$$

-2-2\sqrt{3} ni 4 ga bo'lish.

$$x=\frac{-\sqrt{3}-1}{2}$$

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

$$2x^{2}+2x-1=2\left(x-\frac{\sqrt{3}-1}{2}\right)\left(x-\frac{-\sqrt{3}-1}{2}\right)$$

Baholash

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