x^2-2x-24 eching

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

Omil

$$\left(x-6\right)\left(x+4\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda x^{2}+ax+bx-24 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-2 ab=1\left(-24\right)=-24$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -24-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-24 2,-12 3,-8 4,-6$$

Har bir juftlik yigʻindisini hisoblang.

$$1-24=-23 2-12=-10 3-8=-5 4-6=-2$$

Yechim – -2 yigʻindisini beruvchi juftlik.

$$a=-6 b=4$$

x^{2}-2x-24 ni \left(x^{2}-6x\right)+\left(4x-24\right) sifatida qaytadan yozish.

$$\left(x^{2}-6x\right)+\left(4x-24\right)$$

Birinchi guruhda x ni va ikkinchi guruhda 4 ni faktordan chiqaring.

$$x\left(x-6\right)+4\left(x-6\right)$$

Distributiv funktsiyasidan foydalangan holda x-6 umumiy terminini chiqaring.

$$\left(x-6\right)\left(x+4\right)$$

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.

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

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.

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

-2 kvadratini chiqarish.

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

-4 ni -24 marotabaga ko'paytirish.

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

4 ni 96 ga qo'shish.

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

100 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±10}{2}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±10}{2}$$

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

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

12 ni 2 ga bo'lish.

$$x=6$$

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

$$x=-\frac{8}{2}$$

-8 ni 2 ga bo'lish.

$$x=-4$$

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 -4 ga bo‘ling.

$$x^{2}-2x-24=\left(x-6\right)\left(x-\left(-4\right)\right)$$

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

$$x^{2}-2x-24=\left(x-6\right)\left(x+4\right)$$

Baholash

$$\left(x-6\right)\left(x+4\right)$$