3x^2-2x-4 eching

$$3 x ^ { 2 } - 2 x - 4$$

Omil

$$3\left(x-\frac{1-\sqrt{13}}{3}\right)\left(x-\frac{\sqrt{13}+1}{3}\right)$$

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.

$$3x^{2}-2x-4=0$$

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.

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

-2 kvadratini chiqarish.

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

-4 ni 3 marotabaga ko'paytirish.

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

-12 ni -4 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+48}}{2\times 3}$$

4 ni 48 ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{52}}{2\times 3}$$

52 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±2\sqrt{13}}{2\times 3}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±2\sqrt{13}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{2±2\sqrt{13}}{6}$$

x=\frac{2±2\sqrt{13}}{6} tenglamasini yeching, bunda ± musbat. 2 ni 2\sqrt{13} ga qo'shish.

$$x=\frac{2\sqrt{13}+2}{6}$$

2+2\sqrt{13} ni 6 ga bo'lish.

$$x=\frac{\sqrt{13}+1}{3}$$

x=\frac{2±2\sqrt{13}}{6} tenglamasini yeching, bunda ± manfiy. 2 dan 2\sqrt{13} ni ayirish.

$$x=\frac{2-2\sqrt{13}}{6}$$

2-2\sqrt{13} ni 6 ga bo'lish.

$$x=\frac{1-\sqrt{13}}{3}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{1+\sqrt{13}}{3} ga va x_{2} uchun \frac{1-\sqrt{13}}{3} ga bo‘ling.

$$3x^{2}-2x-4=3\left(x-\frac{\sqrt{13}+1}{3}\right)\left(x-\frac{1-\sqrt{13}}{3}\right)$$

Baholash

$$3x^{2}-2x-4$$