x^2-2x-120= eching

$$x ^ { 2 } - 2 x - 120 =$$

Omil

$$\left(x-12\right)\left(x+10\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda x^{2}+ax+bx-120 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-2 ab=1\left(-120\right)=-120$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -120-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-120 2,-60 3,-40 4,-30 5,-24 6,-20 8,-15 10,-12$$

Har bir juftlik yigʻindisini hisoblang.

$$1-120=-119 2-60=-58 3-40=-37 4-30=-26 5-24=-19 6-20=-14 8-15=-7 10-12=-2$$

Yechim – -2 yigʻindisini beruvchi juftlik.

$$a=-12 b=10$$

x^{2}-2x-120 ni \left(x^{2}-12x\right)+\left(10x-120\right) sifatida qaytadan yozish.

$$\left(x^{2}-12x\right)+\left(10x-120\right)$$

Birinchi guruhda x ni va ikkinchi guruhda 10 ni faktordan chiqaring.

$$x\left(x-12\right)+10\left(x-12\right)$$

Distributiv funktsiyasidan foydalangan holda x-12 umumiy terminini chiqaring.

$$\left(x-12\right)\left(x+10\right)$$

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.

$$x^{2}-2x-120=0$$

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.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-120\right)}}{2}$$

-2 kvadratini chiqarish.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-120\right)}}{2}$$

-4 ni -120 marotabaga ko'paytirish.

$$x=\frac{-\left(-2\right)±\sqrt{4+480}}{2}$$

4 ni 480 ga qo'shish.

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

484 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±22}{2}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±22}{2}$$

x=\frac{2±22}{2} tenglamasini yeching, bunda ± musbat. 2 ni 22 ga qo'shish.

$$x=\frac{24}{2}$$

24 ni 2 ga bo'lish.

$$x=12$$

x=\frac{2±22}{2} tenglamasini yeching, bunda ± manfiy. 2 dan 22 ni ayirish.

$$x=-\frac{20}{2}$$

-20 ni 2 ga bo'lish.

$$x=-10$$

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 -10 ga bo‘ling.

$$x^{2}-2x-120=\left(x-12\right)\left(x-\left(-10\right)\right)$$

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

$$x^{2}-2x-120=\left(x-12\right)\left(x+10\right)$$

Baholash

$$\left(x-12\right)\left(x+10\right)$$