2x^2+5x-4 eching

$$2 x ^ { 2 } + 5 x - 4$$

Omil

$$2\left(x-\frac{-\sqrt{57}-5}{4}\right)\left(x-\frac{\sqrt{57}-5}{4}\right)$$

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.

$$2x^{2}+5x-4=0$$

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.

$$x=\frac{-5±\sqrt{5^{2}-4\times 2\left(-4\right)}}{2\times 2}$$

5 kvadratini chiqarish.

$$x=\frac{-5±\sqrt{25-4\times 2\left(-4\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{25-8\left(-4\right)}}{2\times 2}$$

-8 ni -4 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{25+32}}{2\times 2}$$

25 ni 32 ga qo'shish.

$$x=\frac{-5±\sqrt{57}}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{57}}{4}$$

x=\frac{-5±\sqrt{57}}{4} tenglamasini yeching, bunda ± musbat. -5 ni \sqrt{57} ga qo'shish.

$$x=\frac{\sqrt{57}-5}{4}$$

x=\frac{-5±\sqrt{57}}{4} tenglamasini yeching, bunda ± manfiy. -5 dan \sqrt{57} ni ayirish.

$$x=\frac{-\sqrt{57}-5}{4}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-5+\sqrt{57}}{4} ga va x_{2} uchun \frac{-5-\sqrt{57}}{4} ga bo‘ling.

$$2x^{2}+5x-4=2\left(x-\frac{\sqrt{57}-5}{4}\right)\left(x-\frac{-\sqrt{57}-5}{4}\right)$$

Baholash

$$2x^{2}+5x-4$$