f(x)=3x^2-24x+12 eching

$$f ( x ) = 3 x ^ { 2 } - 24 x + 12$$

Omil

$$3\left(x-\left(4-2\sqrt{3}\right)\right)\left(x-\left(2\sqrt{3}+4\right)\right)$$

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.

$$3x^{2}-24x+12=0$$

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.

$$x=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}-4\times 3\times 12}}{2\times 3}$$

-24 kvadratini chiqarish.

$$x=\frac{-\left(-24\right)±\sqrt{576-4\times 3\times 12}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-24\right)±\sqrt{576-12\times 12}}{2\times 3}$$

-12 ni 12 marotabaga ko'paytirish.

$$x=\frac{-\left(-24\right)±\sqrt{576-144}}{2\times 3}$$

576 ni -144 ga qo'shish.

$$x=\frac{-\left(-24\right)±\sqrt{432}}{2\times 3}$$

432 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-24\right)±12\sqrt{3}}{2\times 3}$$

-24 ning teskarisi 24 ga teng.

$$x=\frac{24±12\sqrt{3}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{24±12\sqrt{3}}{6}$$

x=\frac{24±12\sqrt{3}}{6} tenglamasini yeching, bunda ± musbat. 24 ni 12\sqrt{3} ga qo'shish.

$$x=\frac{12\sqrt{3}+24}{6}$$

24+12\sqrt{3} ni 6 ga bo'lish.

$$x=2\sqrt{3}+4$$

x=\frac{24±12\sqrt{3}}{6} tenglamasini yeching, bunda ± manfiy. 24 dan 12\sqrt{3} ni ayirish.

$$x=\frac{24-12\sqrt{3}}{6}$$

24-12\sqrt{3} ni 6 ga bo'lish.

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

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 4+2\sqrt{3} ga va x_{2} uchun 4-2\sqrt{3} ga bo‘ling.

$$3x^{2}-24x+12=3\left(x-\left(2\sqrt{3}+4\right)\right)\left(x-\left(4-2\sqrt{3}\right)\right)$$

Baholash

$$3\left(x^{2}-8x+4\right)$$