3x^2-x-5 eching

$$3 x ^ { 2 } - x - 5$$

Omil

$$3\left(x-\frac{1-\sqrt{61}}{6}\right)\left(x-\frac{\sqrt{61}+1}{6}\right)$$

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.

$$3x^{2}-x-5=0$$

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.

$$x=\frac{-\left(-1\right)±\sqrt{1-4\times 3\left(-5\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1-12\left(-5\right)}}{2\times 3}$$

-12 ni -5 marotabaga ko'paytirish.

$$x=\frac{-\left(-1\right)±\sqrt{1+60}}{2\times 3}$$

1 ni 60 ga qo'shish.

$$x=\frac{-\left(-1\right)±\sqrt{61}}{2\times 3}$$

-1 ning teskarisi 1 ga teng.

$$x=\frac{1±\sqrt{61}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{1±\sqrt{61}}{6}$$

x=\frac{1±\sqrt{61}}{6} tenglamasini yeching, bunda ± musbat. 1 ni \sqrt{61} ga qo'shish.

$$x=\frac{\sqrt{61}+1}{6}$$

x=\frac{1±\sqrt{61}}{6} tenglamasini yeching, bunda ± manfiy. 1 dan \sqrt{61} ni ayirish.

$$x=\frac{1-\sqrt{61}}{6}$$

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{61}}{6} ga va x_{2} uchun \frac{1-\sqrt{61}}{6} ga bo‘ling.

$$3x^{2}-x-5=3\left(x-\frac{\sqrt{61}+1}{6}\right)\left(x-\frac{1-\sqrt{61}}{6}\right)$$

Baholash

$$3x^{2}-x-5$$