F(x)=-x^2-2x+4 eching

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

Omil

$$-\left(x-\left(-\sqrt{5}-1\right)\right)\left(x-\left(\sqrt{5}-1\right)\right)$$

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.

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

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.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-1\right)\times 4}}{2\left(-1\right)}$$

-2 kvadratini chiqarish.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-1\right)\times 4}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+4\times 4}}{2\left(-1\right)}$$

4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+16}}{2\left(-1\right)}$$

4 ni 16 ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{20}}{2\left(-1\right)}$$

20 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±2\sqrt{5}}{2\left(-1\right)}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±2\sqrt{5}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{2±2\sqrt{5}}{-2}$$

x=\frac{2±2\sqrt{5}}{-2} tenglamasini yeching, bunda ± musbat. 2 ni 2\sqrt{5} ga qo'shish.

$$x=\frac{2\sqrt{5}+2}{-2}$$

2+2\sqrt{5} ni -2 ga bo'lish.

$$x=-\left(\sqrt{5}+1\right)$$

x=\frac{2±2\sqrt{5}}{-2} tenglamasini yeching, bunda ± manfiy. 2 dan 2\sqrt{5} ni ayirish.

$$x=\frac{2-2\sqrt{5}}{-2}$$

2-2\sqrt{5} ni -2 ga bo'lish.

$$x=\sqrt{5}-1$$

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

$$-x^{2}-2x+4=-\left(x-\left(-\left(\sqrt{5}+1\right)\right)\right)\left(x-\left(\sqrt{5}-1\right)\right)$$

Baholash

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