4x^2-12x-3 eching

$$4 x ^ { 2 } - 12 x - 3$$

Omil

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

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.

$$4x^{2}-12x-3=0$$

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.

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

-12 kvadratini chiqarish.

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

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-\left(-12\right)±\sqrt{144-16\left(-3\right)}}{2\times 4}$$

-16 ni -3 marotabaga ko'paytirish.

$$x=\frac{-\left(-12\right)±\sqrt{144+48}}{2\times 4}$$

144 ni 48 ga qo'shish.

$$x=\frac{-\left(-12\right)±\sqrt{192}}{2\times 4}$$

192 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-12\right)±8\sqrt{3}}{2\times 4}$$

-12 ning teskarisi 12 ga teng.

$$x=\frac{12±8\sqrt{3}}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{12±8\sqrt{3}}{8}$$

x=\frac{12±8\sqrt{3}}{8} tenglamasini yeching, bunda ± musbat. 12 ni 8\sqrt{3} ga qo'shish.

$$x=\frac{8\sqrt{3}+12}{8}$$

12+8\sqrt{3} ni 8 ga bo'lish.

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

x=\frac{12±8\sqrt{3}}{8} tenglamasini yeching, bunda ± manfiy. 12 dan 8\sqrt{3} ni ayirish.

$$x=\frac{12-8\sqrt{3}}{8}$$

12-8\sqrt{3} ni 8 ga bo'lish.

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

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

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

Baholash

$$4x^{2}-12x-3$$