x^2-2x-3 eching

$${ x }^{ 2 } -2x-3$$

Omil

$$\left(x-3\right)\left(x+1\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda x^{2}+ax+bx-3 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-2 ab=1\left(-3\right)=-3$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. Faqat bundan juftlik tizim yechimidir.

$$a=-3 b=1$$

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

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

x^{2}-3x ichida x ni ajrating.

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

Distributiv funktsiyasidan foydalangan holda x-3 umumiy terminini chiqaring.

$$\left(x-3\right)\left(x+1\right)$$

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.

$$x^{2}-2x-3=0$$

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.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-3\right)}}{2}$$

-2 kvadratini chiqarish.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\left(-3\right)}}{2}$$

-4 ni -3 marotabaga ko'paytirish.

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

4 ni 12 ga qo'shish.

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

16 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-2\right)±4}{2}$$

-2 ning teskarisi 2 ga teng.

$$x=\frac{2±4}{2}$$

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

$$x=\frac{6}{2}$$

6 ni 2 ga bo'lish.

$$x=3$$

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

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

-2 ni 2 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 3 ga va x_{2} uchun -1 ga bo‘ling.

$$x^{2}-2x-3=\left(x-3\right)\left(x-\left(-1\right)\right)$$

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

$$x^{2}-2x-3=\left(x-3\right)\left(x+1\right)$$

Baholash

$$\left(x-3\right)\left(x+1\right)$$