f(x)=3x^2+12x+5 eching

$$f ( x ) = 3 x ^ { 2 } + 12 x + 5$$

Omil

$$3\left(x-\left(-\frac{\sqrt{21}}{3}-2\right)\right)\left(x-\left(\frac{\sqrt{21}}{3}-2\right)\right)$$

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.

$$3x^{2}+12x+5=0$$

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.

$$x=\frac{-12±\sqrt{12^{2}-4\times 3\times 5}}{2\times 3}$$

12 kvadratini chiqarish.

$$x=\frac{-12±\sqrt{144-4\times 3\times 5}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144-12\times 5}}{2\times 3}$$

-12 ni 5 marotabaga ko'paytirish.

$$x=\frac{-12±\sqrt{144-60}}{2\times 3}$$

144 ni -60 ga qo'shish.

$$x=\frac{-12±\sqrt{84}}{2\times 3}$$

84 ning kvadrat ildizini chiqarish.

$$x=\frac{-12±2\sqrt{21}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{-12±2\sqrt{21}}{6}$$

x=\frac{-12±2\sqrt{21}}{6} tenglamasini yeching, bunda ± musbat. -12 ni 2\sqrt{21} ga qo'shish.

$$x=\frac{2\sqrt{21}-12}{6}$$

-12+2\sqrt{21} ni 6 ga bo'lish.

$$x=\frac{\sqrt{21}}{3}-2$$

x=\frac{-12±2\sqrt{21}}{6} tenglamasini yeching, bunda ± manfiy. -12 dan 2\sqrt{21} ni ayirish.

$$x=\frac{-2\sqrt{21}-12}{6}$$

-12-2\sqrt{21} ni 6 ga bo'lish.

$$x=-\frac{\sqrt{21}}{3}-2$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -2+\frac{\sqrt{21}}{3} ga va x_{2} uchun -2-\frac{\sqrt{21}}{3} ga bo‘ling.

$$3x^{2}+12x+5=3\left(x-\left(\frac{\sqrt{21}}{3}-2\right)\right)\left(x-\left(-\frac{\sqrt{21}}{3}-2\right)\right)$$

Baholash

$$3x^{2}+12x+5$$