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

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

Omil

$$-2\left(x-\frac{3-\sqrt{19}}{2}\right)\left(x-\frac{\sqrt{19}+3}{2}\right)$$

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.

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

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.

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

6 kvadratini chiqarish.

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

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36+8\times 5}}{2\left(-2\right)}$$

8 ni 5 marotabaga ko'paytirish.

$$x=\frac{-6±\sqrt{36+40}}{2\left(-2\right)}$$

36 ni 40 ga qo'shish.

$$x=\frac{-6±\sqrt{76}}{2\left(-2\right)}$$

76 ning kvadrat ildizini chiqarish.

$$x=\frac{-6±2\sqrt{19}}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-6±2\sqrt{19}}{-4}$$

x=\frac{-6±2\sqrt{19}}{-4} tenglamasini yeching, bunda ± musbat. -6 ni 2\sqrt{19} ga qo'shish.

$$x=\frac{2\sqrt{19}-6}{-4}$$

-6+2\sqrt{19} ni -4 ga bo'lish.

$$x=\frac{3-\sqrt{19}}{2}$$

x=\frac{-6±2\sqrt{19}}{-4} tenglamasini yeching, bunda ± manfiy. -6 dan 2\sqrt{19} ni ayirish.

$$x=\frac{-2\sqrt{19}-6}{-4}$$

-6-2\sqrt{19} ni -4 ga bo'lish.

$$x=\frac{\sqrt{19}+3}{2}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{3-\sqrt{19}}{2} ga va x_{2} uchun \frac{3+\sqrt{19}}{2} ga bo‘ling.

$$-2x^{2}+6x+5=-2\left(x-\frac{3-\sqrt{19}}{2}\right)\left(x-\frac{\sqrt{19}+3}{2}\right)$$

Baholash

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