3x^2+4x-1 eching

$$3 x ^ { 2 } + 4 x - 1$$

Omil

$$3\left(x-\frac{-\sqrt{7}-2}{3}\right)\left(x-\frac{\sqrt{7}-2}{3}\right)$$

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.

$$3x^{2}+4x-1=0$$

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.

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

4 kvadratini chiqarish.

$$x=\frac{-4±\sqrt{16-4\times 3\left(-1\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16-12\left(-1\right)}}{2\times 3}$$

-12 ni -1 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16+12}}{2\times 3}$$

16 ni 12 ga qo'shish.

$$x=\frac{-4±\sqrt{28}}{2\times 3}$$

28 ning kvadrat ildizini chiqarish.

$$x=\frac{-4±2\sqrt{7}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{-4±2\sqrt{7}}{6}$$

x=\frac{-4±2\sqrt{7}}{6} tenglamasini yeching, bunda ± musbat. -4 ni 2\sqrt{7} ga qo'shish.

$$x=\frac{2\sqrt{7}-4}{6}$$

-4+2\sqrt{7} ni 6 ga bo'lish.

$$x=\frac{\sqrt{7}-2}{3}$$

x=\frac{-4±2\sqrt{7}}{6} tenglamasini yeching, bunda ± manfiy. -4 dan 2\sqrt{7} ni ayirish.

$$x=\frac{-2\sqrt{7}-4}{6}$$

-4-2\sqrt{7} ni 6 ga bo'lish.

$$x=\frac{-\sqrt{7}-2}{3}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-2+\sqrt{7}}{3} ga va x_{2} uchun \frac{-2-\sqrt{7}}{3} ga bo‘ling.

$$3x^{2}+4x-1=3\left(x-\frac{\sqrt{7}-2}{3}\right)\left(x-\frac{-\sqrt{7}-2}{3}\right)$$

Baholash

$$3x^{2}+4x-1$$