f(x)=-x^2+6x+5 eching

$$f ( x ) = - x ^ { 2 } + 6 x + 5$$

Omil

$$-\left(x-\left(3-\sqrt{14}\right)\right)\left(x-\left(\sqrt{14}+3\right)\right)$$

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.

$$-x^{2}+6x+5=0$$

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.

$$x=\frac{-6±\sqrt{6^{2}-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

6 kvadratini chiqarish.

$$x=\frac{-6±\sqrt{36-4\left(-1\right)\times 5}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36+4\times 5}}{2\left(-1\right)}$$

4 ni 5 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36+20}}{2\left(-1\right)}$$

36 ni 20 ga qo'shish.

$$x=\frac{-6±\sqrt{56}}{2\left(-1\right)}$$

56 ning kvadrat ildizini chiqarish.

$$x=\frac{-6±2\sqrt{14}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-6±2\sqrt{14}}{-2}$$

x=\frac{-6±2\sqrt{14}}{-2} tenglamasini yeching, bunda ± musbat. -6 ni 2\sqrt{14} ga qo'shish.

$$x=\frac{2\sqrt{14}-6}{-2}$$

-6+2\sqrt{14} ni -2 ga bo'lish.

$$x=3-\sqrt{14}$$

x=\frac{-6±2\sqrt{14}}{-2} tenglamasini yeching, bunda ± manfiy. -6 dan 2\sqrt{14} ni ayirish.

$$x=\frac{-2\sqrt{14}-6}{-2}$$

-6-2\sqrt{14} ni -2 ga bo'lish.

$$x=\sqrt{14}+3$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 3-\sqrt{14} ga va x_{2} uchun 3+\sqrt{14} ga bo‘ling.

$$-x^{2}+6x+5=-\left(x-\left(3-\sqrt{14}\right)\right)\left(x-\left(\sqrt{14}+3\right)\right)$$

Baholash

$$5+6x-x^{2}$$