3+12t-4t^2 eching

$$3 + 12 t - 4 t ^ { 2 }$$

Omil

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

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.

$$-4t^{2}+12t+3=0$$

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.

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

12 kvadratini chiqarish.

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

-4 ni -4 marotabaga ko'paytirish.

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

16 ni 3 marotabaga ko'paytirish.

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

144 ni 48 ga qo'shish.

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

192 ning kvadrat ildizini chiqarish.

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

2 ni -4 marotabaga ko'paytirish.

$$t=\frac{-12±8\sqrt{3}}{-8}$$

t=\frac{-12±8\sqrt{3}}{-8} tenglamasini yeching, bunda ± musbat. -12 ni 8\sqrt{3} ga qo'shish.

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

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

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

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

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

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

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

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.

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

Baholash

$$3+12t-4t^{2}$$