f(x)=3x^2+6x-2 eching

$$f ( x ) = 3 x ^ { 2 } + 6 x - 2$$

Omil

$$3\left(x-\left(-\frac{\sqrt{15}}{3}-1\right)\right)\left(x-\left(\frac{\sqrt{15}}{3}-1\right)\right)$$

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.

$$3x^{2}+6x-2=0$$

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.

$$x=\frac{-6±\sqrt{6^{2}-4\times 3\left(-2\right)}}{2\times 3}$$

6 kvadratini chiqarish.

$$x=\frac{-6±\sqrt{36-4\times 3\left(-2\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36-12\left(-2\right)}}{2\times 3}$$

-12 ni -2 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36+24}}{2\times 3}$$

36 ni 24 ga qo'shish.

$$x=\frac{-6±\sqrt{60}}{2\times 3}$$

60 ning kvadrat ildizini chiqarish.

$$x=\frac{-6±2\sqrt{15}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{-6±2\sqrt{15}}{6}$$

x=\frac{-6±2\sqrt{15}}{6} tenglamasini yeching, bunda ± musbat. -6 ni 2\sqrt{15} ga qo'shish.

$$x=\frac{2\sqrt{15}-6}{6}$$

-6+2\sqrt{15} ni 6 ga bo'lish.

$$x=\frac{\sqrt{15}}{3}-1$$

x=\frac{-6±2\sqrt{15}}{6} tenglamasini yeching, bunda ± manfiy. -6 dan 2\sqrt{15} ni ayirish.

$$x=\frac{-2\sqrt{15}-6}{6}$$

-6-2\sqrt{15} ni 6 ga bo'lish.

$$x=-\frac{\sqrt{15}}{3}-1$$

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{15}}{3} ga va x_{2} uchun -1-\frac{\sqrt{15}}{3} ga bo‘ling.

$$3x^{2}+6x-2=3\left(x-\left(\frac{\sqrt{15}}{3}-1\right)\right)\left(x-\left(-\frac{\sqrt{15}}{3}-1\right)\right)$$

Baholash

$$3x^{2}+6x-2$$