-2x^2+4x+3 eching

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

Omil

$$-2\left(x-\left(-\frac{\sqrt{10}}{2}+1\right)\right)\left(x-\left(\frac{\sqrt{10}}{2}+1\right)\right)$$

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.

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

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.

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

4 kvadratini chiqarish.

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

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16+8\times 3}}{2\left(-2\right)}$$

8 ni 3 marotabaga ko'paytirish.

$$x=\frac{-4±\sqrt{16+24}}{2\left(-2\right)}$$

16 ni 24 ga qo'shish.

$$x=\frac{-4±\sqrt{40}}{2\left(-2\right)}$$

40 ning kvadrat ildizini chiqarish.

$$x=\frac{-4±2\sqrt{10}}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-4±2\sqrt{10}}{-4}$$

x=\frac{-4±2\sqrt{10}}{-4} tenglamasini yeching, bunda ± musbat. -4 ni 2\sqrt{10} ga qo'shish.

$$x=\frac{2\sqrt{10}-4}{-4}$$

-4+2\sqrt{10} ni -4 ga bo'lish.

$$x=-\frac{\sqrt{10}}{2}+1$$

x=\frac{-4±2\sqrt{10}}{-4} tenglamasini yeching, bunda ± manfiy. -4 dan 2\sqrt{10} ni ayirish.

$$x=\frac{-2\sqrt{10}-4}{-4}$$

-4-2\sqrt{10} ni -4 ga bo'lish.

$$x=\frac{\sqrt{10}}{2}+1$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 1-\frac{\sqrt{10}}{2} ga va x_{2} uchun 1+\frac{\sqrt{10}}{2} ga bo‘ling.

$$-2x^{2}+4x+3=-2\left(x-\left(-\frac{\sqrt{10}}{2}+1\right)\right)\left(x-\left(\frac{\sqrt{10}}{2}+1\right)\right)$$

Baholash

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