3x^2-12x-11 eching

$$3 x ^ { 2 } - 12 x - 11$$

Omil

$$3\left(x-\left(-\frac{\sqrt{69}}{3}+2\right)\right)\left(x-\left(\frac{\sqrt{69}}{3}+2\right)\right)$$

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.

$$3x^{2}-12x-11=0$$

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.

$$x=\frac{-\left(-12\right)±\sqrt{\left(-12\right)^{2}-4\times 3\left(-11\right)}}{2\times 3}$$

-12 kvadratini chiqarish.

$$x=\frac{-\left(-12\right)±\sqrt{144-4\times 3\left(-11\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-\left(-12\right)±\sqrt{144-12\left(-11\right)}}{2\times 3}$$

-12 ni -11 marotabaga ko'paytirish.

$$x=\frac{-\left(-12\right)±\sqrt{144+132}}{2\times 3}$$

144 ni 132 ga qo'shish.

$$x=\frac{-\left(-12\right)±\sqrt{276}}{2\times 3}$$

276 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-12\right)±2\sqrt{69}}{2\times 3}$$

-12 ning teskarisi 12 ga teng.

$$x=\frac{12±2\sqrt{69}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{12±2\sqrt{69}}{6}$$

x=\frac{12±2\sqrt{69}}{6} tenglamasini yeching, bunda ± musbat. 12 ni 2\sqrt{69} ga qo'shish.

$$x=\frac{2\sqrt{69}+12}{6}$$

12+2\sqrt{69} ni 6 ga bo'lish.

$$x=\frac{\sqrt{69}}{3}+2$$

x=\frac{12±2\sqrt{69}}{6} tenglamasini yeching, bunda ± manfiy. 12 dan 2\sqrt{69} ni ayirish.

$$x=\frac{12-2\sqrt{69}}{6}$$

12-2\sqrt{69} ni 6 ga bo'lish.

$$x=-\frac{\sqrt{69}}{3}+2$$

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{69}}{3} ga va x_{2} uchun 2-\frac{\sqrt{69}}{3} ga bo‘ling.

$$3x^{2}-12x-11=3\left(x-\left(\frac{\sqrt{69}}{3}+2\right)\right)\left(x-\left(-\frac{\sqrt{69}}{3}+2\right)\right)$$

Baholash

$$3x^{2}-12x-11$$