f(x)=-2x^2+8x+4 eching

$$f ( x ) = - 2 x ^ { 2 } + 8 x + 4$$

Omil

$$-2\left(x-\left(2-\sqrt{6}\right)\right)\left(x-\left(\sqrt{6}+2\right)\right)$$

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.

$$-2x^{2}+8x+4=0$$

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.

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

8 kvadratini chiqarish.

$$x=\frac{-8±\sqrt{64-4\left(-2\right)\times 4}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-8±\sqrt{64+8\times 4}}{2\left(-2\right)}$$

8 ni 4 marotabaga ko'paytirish.

$$x=\frac{-8±\sqrt{64+32}}{2\left(-2\right)}$$

64 ni 32 ga qo'shish.

$$x=\frac{-8±\sqrt{96}}{2\left(-2\right)}$$

96 ning kvadrat ildizini chiqarish.

$$x=\frac{-8±4\sqrt{6}}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-8±4\sqrt{6}}{-4}$$

x=\frac{-8±4\sqrt{6}}{-4} tenglamasini yeching, bunda ± musbat. -8 ni 4\sqrt{6} ga qo'shish.

$$x=\frac{4\sqrt{6}-8}{-4}$$

-8+4\sqrt{6} ni -4 ga bo'lish.

$$x=2-\sqrt{6}$$

x=\frac{-8±4\sqrt{6}}{-4} tenglamasini yeching, bunda ± manfiy. -8 dan 4\sqrt{6} ni ayirish.

$$x=\frac{-4\sqrt{6}-8}{-4}$$

-8-4\sqrt{6} ni -4 ga bo'lish.

$$x=\sqrt{6}+2$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 2-\sqrt{6} ga va x_{2} uchun 2+\sqrt{6} ga bo‘ling.

$$-2x^{2}+8x+4=-2\left(x-\left(2-\sqrt{6}\right)\right)\left(x-\left(\sqrt{6}+2\right)\right)$$

Baholash

$$4+8x-2x^{2}$$