4x^2-3x-4 eching

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

Omil

$$4\left(x-\frac{3-\sqrt{73}}{8}\right)\left(x-\frac{\sqrt{73}+3}{8}\right)$$

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.

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

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.

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

-3 kvadratini chiqarish.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\times 4\left(-4\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9-16\left(-4\right)}}{2\times 4}$$

-16 ni -4 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9+64}}{2\times 4}$$

9 ni 64 ga qo'shish.

$$x=\frac{-\left(-3\right)±\sqrt{73}}{2\times 4}$$

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±\sqrt{73}}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{3±\sqrt{73}}{8}$$

x=\frac{3±\sqrt{73}}{8} tenglamasini yeching, bunda ± musbat. 3 ni \sqrt{73} ga qo'shish.

$$x=\frac{\sqrt{73}+3}{8}$$

x=\frac{3±\sqrt{73}}{8} tenglamasini yeching, bunda ± manfiy. 3 dan \sqrt{73} ni ayirish.

$$x=\frac{3-\sqrt{73}}{8}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{3+\sqrt{73}}{8} ga va x_{2} uchun \frac{3-\sqrt{73}}{8} ga bo‘ling.

$$4x^{2}-3x-4=4\left(x-\frac{\sqrt{73}+3}{8}\right)\left(x-\frac{3-\sqrt{73}}{8}\right)$$

Baholash

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