T(x)=-x^2+3x-2 eching

$$T ( x ) = - x ^ { 2 } + 3 x - 2$$

Omil

$$\left(1-x\right)\left(x-2\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda -x^{2}+ax+bx-2 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=3 ab=-\left(-2\right)=2$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b musbat boʻlganda, a va b ikkisi ham musbat. Faqat bundan juftlik tizim yechimidir.

$$a=2 b=1$$

-x^{2}+3x-2 ni \left(-x^{2}+2x\right)+\left(x-2\right) sifatida qaytadan yozish.

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

-x^{2}+2x ichida -x ni ajrating.

$$-x\left(x-2\right)+x-2$$

Distributiv funktsiyasidan foydalangan holda x-2 umumiy terminini chiqaring.

$$\left(x-2\right)\left(-x+1\right)$$

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.

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

3 kvadratini chiqarish.

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

-4 ni -1 marotabaga ko'paytirish.

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

4 ni -2 marotabaga ko'paytirish.

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

9 ni -8 ga qo'shish.

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

1 ning kvadrat ildizini chiqarish.

$$x=\frac{-3±1}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{-3±1}{-2}$$

x=\frac{-3±1}{-2} tenglamasini yeching, bunda ± musbat. -3 ni 1 ga qo'shish.

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

-2 ni -2 ga bo'lish.

$$x=1$$

x=\frac{-3±1}{-2} tenglamasini yeching, bunda ± manfiy. -3 dan 1 ni ayirish.

$$x=-\frac{4}{-2}$$

-4 ni -2 ga bo'lish.

$$x=2$$

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

$$-x^{2}+3x-2=-\left(x-1\right)\left(x-2\right)$$

Baholash

$$\left(1-x\right)\left(x-2\right)$$