2x^2-2x-12 eching

$$2 x ^ { 2 } - 2 x - 12$$

Omil

$$2\left(x-3\right)\left(x+2\right)$$

Yechim qadamlari

2 omili.

$$2\left(x^{2}-x-6\right)$$

Hisoblang: x^{2}-x-6. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda x^{2}+ax+bx-6 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-1 ab=1\left(-6\right)=-6$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -6-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-6 2,-3$$

Har bir juftlik yigʻindisini hisoblang.

$$1-6=-5 2-3=-1$$

Yechim – -1 yigʻindisini beruvchi juftlik.

$$a=-3 b=2$$

x^{2}-x-6 ni \left(x^{2}-3x\right)+\left(2x-6\right) sifatida qaytadan yozish.

$$\left(x^{2}-3x\right)+\left(2x-6\right)$$

Birinchi guruhda x ni va ikkinchi guruhda 2 ni faktordan chiqaring.

$$x\left(x-3\right)+2\left(x-3\right)$$

Distributiv funktsiyasidan foydalangan holda x-3 umumiy terminini chiqaring.

$$\left(x-3\right)\left(x+2\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$2\left(x-3\right)\left(x+2\right)$$

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.

$$2x^{2}-2x-12=0$$

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.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 2\left(-12\right)}}{2\times 2}$$

-2 kvadratini chiqarish.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\times 2\left(-12\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4-8\left(-12\right)}}{2\times 2}$$

-8 ni -12 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+96}}{2\times 2}$$

4 ni 96 ga qo'shish.

$$x=\frac{-\left(-2\right)±\sqrt{100}}{2\times 2}$$

100 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±10}{2\times 2}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±10}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$x=\frac{2±10}{4}$$

x=\frac{2±10}{4} tenglamasini yeching, bunda ± musbat. 2 ni 10 ga qo'shish.

$$x=\frac{12}{4}$$

12 ni 4 ga bo'lish.

$$x=3$$

x=\frac{2±10}{4} tenglamasini yeching, bunda ± manfiy. 2 dan 10 ni ayirish.

$$x=-\frac{8}{4}$$

-8 ni 4 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 3 ga va x_{2} uchun -2 ga bo‘ling.

$$2x^{2}-2x-12=2\left(x-3\right)\left(x-\left(-2\right)\right)$$

p-\left(-q\right) shaklining barcha amallarigani p+q ga soddalashtiring.

$$2x^{2}-2x-12=2\left(x-3\right)\left(x+2\right)$$

Baholash

$$2\left(x-3\right)\left(x+2\right)$$