4t^2+16t+9 eching

$$4 t ^ { 2 } + 16 t + 9$$

Omil

$$4\left(t-\left(-\frac{\sqrt{7}}{2}-2\right)\right)\left(t-\left(\frac{\sqrt{7}}{2}-2\right)\right)$$

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.

$$4t^{2}+16t+9=0$$

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.

$$t=\frac{-16±\sqrt{16^{2}-4\times 4\times 9}}{2\times 4}$$

16 kvadratini chiqarish.

$$t=\frac{-16±\sqrt{256-4\times 4\times 9}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$t=\frac{-16±\sqrt{256-16\times 9}}{2\times 4}$$

-16 ni 9 marotabaga ko'paytirish.

$$t=\frac{-16±\sqrt{256-144}}{2\times 4}$$

256 ni -144 ga qo'shish.

$$t=\frac{-16±\sqrt{112}}{2\times 4}$$

112 ning kvadrat ildizini chiqarish.

$$t=\frac{-16±4\sqrt{7}}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$t=\frac{-16±4\sqrt{7}}{8}$$

t=\frac{-16±4\sqrt{7}}{8} tenglamasini yeching, bunda ± musbat. -16 ni 4\sqrt{7} ga qo'shish.

$$t=\frac{4\sqrt{7}-16}{8}$$

-16+4\sqrt{7} ni 8 ga bo'lish.

$$t=\frac{\sqrt{7}}{2}-2$$

t=\frac{-16±4\sqrt{7}}{8} tenglamasini yeching, bunda ± manfiy. -16 dan 4\sqrt{7} ni ayirish.

$$t=\frac{-4\sqrt{7}-16}{8}$$

-16-4\sqrt{7} ni 8 ga bo'lish.

$$t=-\frac{\sqrt{7}}{2}-2$$

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{7}}{2} ga va x_{2} uchun -2-\frac{\sqrt{7}}{2} ga bo‘ling.

$$4t^{2}+16t+9=4\left(t-\left(\frac{\sqrt{7}}{2}-2\right)\right)\left(t-\left(-\frac{\sqrt{7}}{2}-2\right)\right)$$

Baholash

$$4t^{2}+16t+9$$