-x^2+3x+2 eching

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

Omil

$$-\left(x-\frac{3-\sqrt{17}}{2}\right)\left(x-\frac{\sqrt{17}+3}{2}\right)$$

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.

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

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.

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

3 kvadratini chiqarish.

$$x=\frac{-3±\sqrt{9-4\left(-1\right)\times 2}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9+4\times 2}}{2\left(-1\right)}$$

4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{9+8}}{2\left(-1\right)}$$

9 ni 8 ga qo'shish.

$$x=\frac{-3±\sqrt{17}}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-3±\sqrt{17}}{-2}$$

x=\frac{-3±\sqrt{17}}{-2} tenglamasini yeching, bunda ± musbat. -3 ni \sqrt{17} ga qo'shish.

$$x=\frac{\sqrt{17}-3}{-2}$$

-3+\sqrt{17} ni -2 ga bo'lish.

$$x=\frac{3-\sqrt{17}}{2}$$

x=\frac{-3±\sqrt{17}}{-2} tenglamasini yeching, bunda ± manfiy. -3 dan \sqrt{17} ni ayirish.

$$x=\frac{-\sqrt{17}-3}{-2}$$

-3-\sqrt{17} ni -2 ga bo'lish.

$$x=\frac{\sqrt{17}+3}{2}$$

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{17}}{2} ga va x_{2} uchun \frac{3+\sqrt{17}}{2} ga bo‘ling.

$$-x^{2}+3x+2=-\left(x-\frac{3-\sqrt{17}}{2}\right)\left(x-\frac{\sqrt{17}+3}{2}\right)$$

Baholash

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