-2x^2-22x+24 eching

$$- 2 x ^ { 2 } - 22 x + 24$$

Omil

$$2\left(1-x\right)\left(x+12\right)$$

Yechim qadamlari

2 omili.

$$2\left(-x^{2}-11x+12\right)$$

Hisoblang: -x^{2}-11x+12. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda -x^{2}+ax+bx+12 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-11 ab=-12=-12$$

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 – -11 yigʻindisini beruvchi juftlik.

$$a=1 b=-12$$

-x^{2}-11x+12 ni \left(-x^{2}+x\right)+\left(-12x+12\right) sifatida qaytadan yozish.

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

Birinchi guruhda x ni va ikkinchi guruhda 12 ni faktordan chiqaring.

$$x\left(-x+1\right)+12\left(-x+1\right)$$

Distributiv funktsiyasidan foydalangan holda -x+1 umumiy terminini chiqaring.

$$\left(-x+1\right)\left(x+12\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$2\left(-x+1\right)\left(x+12\right)$$

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.

$$-2x^{2}-22x+24=0$$

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.

$$x=\frac{-\left(-22\right)±\sqrt{\left(-22\right)^{2}-4\left(-2\right)\times 24}}{2\left(-2\right)}$$

-22 kvadratini chiqarish.

$$x=\frac{-\left(-22\right)±\sqrt{484-4\left(-2\right)\times 24}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-\left(-22\right)±\sqrt{484+8\times 24}}{2\left(-2\right)}$$

8 ni 24 marotabaga ko'paytirish.

$$x=\frac{-\left(-22\right)±\sqrt{484+192}}{2\left(-2\right)}$$

484 ni 192 ga qo'shish.

$$x=\frac{-\left(-22\right)±\sqrt{676}}{2\left(-2\right)}$$

676 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-22\right)±26}{2\left(-2\right)}$$

-22 ning teskarisi 22 ga teng.

$$x=\frac{22±26}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{22±26}{-4}$$

x=\frac{22±26}{-4} tenglamasini yeching, bunda ± musbat. 22 ni 26 ga qo'shish.

$$x=\frac{48}{-4}$$

48 ni -4 ga bo'lish.

$$x=-12$$

x=\frac{22±26}{-4} tenglamasini yeching, bunda ± manfiy. 22 dan 26 ni ayirish.

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

-4 ni -4 ga bo'lish.

$$x=1$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -12 ga va x_{2} uchun 1 ga bo‘ling.

$$-2x^{2}-22x+24=-2\left(x-\left(-12\right)\right)\left(x-1\right)$$

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

$$-2x^{2}-22x+24=-2\left(x+12\right)\left(x-1\right)$$

Baholash

$$2\left(1-x\right)\left(x+12\right)$$