f(x)=-x^2-4x+12 eching

$$f ( x ) = - x ^ { 2 } - 4 x + 12$$

Omil

$$\left(2-x\right)\left(x+6\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda -x^{2}+ax+bx+12 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-4 ab=-12=-12$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -12-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-12 2,-6 3,-4$$

Har bir juftlik yigʻindisini hisoblang.

$$1-12=-11 2-6=-4 3-4=-1$$

Yechim – -4 yigʻindisini beruvchi juftlik.

$$a=2 b=-6$$

-x^{2}-4x+12 ni \left(-x^{2}+2x\right)+\left(-6x+12\right) sifatida qaytadan yozish.

$$\left(-x^{2}+2x\right)+\left(-6x+12\right)$$

Birinchi guruhda x ni va ikkinchi guruhda 6 ni faktordan chiqaring.

$$x\left(-x+2\right)+6\left(-x+2\right)$$

Distributiv funktsiyasidan foydalangan holda -x+2 umumiy terminini chiqaring.

$$\left(-x+2\right)\left(x+6\right)$$

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.

$$-x^{2}-4x+12=0$$

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.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-1\right)\times 12}}{2\left(-1\right)}$$

-4 kvadratini chiqarish.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\left(-1\right)\times 12}}{2\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16+4\times 12}}{2\left(-1\right)}$$

4 ni 12 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16+48}}{2\left(-1\right)}$$

16 ni 48 ga qo'shish.

$$x=\frac{-\left(-4\right)±\sqrt{64}}{2\left(-1\right)}$$

64 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-4\right)±8}{2\left(-1\right)}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±8}{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$x=\frac{4±8}{-2}$$

x=\frac{4±8}{-2} tenglamasini yeching, bunda ± musbat. 4 ni 8 ga qo'shish.

$$x=\frac{12}{-2}$$

12 ni -2 ga bo'lish.

$$x=-6$$

x=\frac{4±8}{-2} tenglamasini yeching, bunda ± manfiy. 4 dan 8 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 -6 ga va x_{2} uchun 2 ga bo‘ling.

$$-x^{2}-4x+12=-\left(x-\left(-6\right)\right)\left(x-2\right)$$

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

$$-x^{2}-4x+12=-\left(x+6\right)\left(x-2\right)$$

Baholash

$$\left(2-x\right)\left(x+6\right)$$