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

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

Omil

$$3\left(x-\left(-\frac{\sqrt{33}}{6}-\frac{1}{2}\right)\right)\left(x-\left(\frac{\sqrt{33}}{6}-\frac{1}{2}\right)\right)$$

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.

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

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.

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

3 kvadratini chiqarish.

$$x=\frac{-3±\sqrt{9-4\times 3\left(-2\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9-12\left(-2\right)}}{2\times 3}$$

-12 ni -2 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9+24}}{2\times 3}$$

9 ni 24 ga qo'shish.

$$x=\frac{-3±\sqrt{33}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{33}}{6}$$

x=\frac{-3±\sqrt{33}}{6} tenglamasini yeching, bunda ± musbat. -3 ni \sqrt{33} ga qo'shish.

$$x=\frac{\sqrt{33}-3}{6}$$

-3+\sqrt{33} ni 6 ga bo'lish.

$$x=\frac{\sqrt{33}}{6}-\frac{1}{2}$$

x=\frac{-3±\sqrt{33}}{6} tenglamasini yeching, bunda ± manfiy. -3 dan \sqrt{33} ni ayirish.

$$x=\frac{-\sqrt{33}-3}{6}$$

-3-\sqrt{33} ni 6 ga bo'lish.

$$x=-\frac{\sqrt{33}}{6}-\frac{1}{2}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -\frac{1}{2}+\frac{\sqrt{33}}{6} ga va x_{2} uchun -\frac{1}{2}-\frac{\sqrt{33}}{6} ga bo‘ling.

$$3x^{2}+3x-2=3\left(x-\left(\frac{\sqrt{33}}{6}-\frac{1}{2}\right)\right)\left(x-\left(-\frac{\sqrt{33}}{6}-\frac{1}{2}\right)\right)$$

Baholash

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