f(x)=3x^2+6x-1 eching

$$f ( x ) = 3 x ^ { 2 } + 6 x - 1$$

Omil

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

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.

$$3x^{2}+6x-1=0$$

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.

$$x=\frac{-6±\sqrt{6^{2}-4\times 3\left(-1\right)}}{2\times 3}$$

6 kvadratini chiqarish.

$$x=\frac{-6±\sqrt{36-4\times 3\left(-1\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36-12\left(-1\right)}}{2\times 3}$$

-12 ni -1 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36+12}}{2\times 3}$$

36 ni 12 ga qo'shish.

$$x=\frac{-6±\sqrt{48}}{2\times 3}$$

48 ning kvadrat ildizini chiqarish.

$$x=\frac{-6±4\sqrt{3}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{-6±4\sqrt{3}}{6}$$

x=\frac{-6±4\sqrt{3}}{6} tenglamasini yeching, bunda ± musbat. -6 ni 4\sqrt{3} ga qo'shish.

$$x=\frac{4\sqrt{3}-6}{6}$$

-6+4\sqrt{3} ni 6 ga bo'lish.

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

x=\frac{-6±4\sqrt{3}}{6} tenglamasini yeching, bunda ± manfiy. -6 dan 4\sqrt{3} ni ayirish.

$$x=\frac{-4\sqrt{3}-6}{6}$$

-6-4\sqrt{3} ni 6 ga bo'lish.

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

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

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

Baholash

$$3x^{2}+6x-1$$