f(x)=x^2-6x-7 eching

$$f ( x ) = x ^ { 2 } - 6 x - 7$$

Omil

$$\left(x-7\right)\left(x+1\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda x^{2}+ax+bx-7 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-6 ab=1\left(-7\right)=-7$$

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.

$$a=-7 b=1$$

x^{2}-6x-7 ni \left(x^{2}-7x\right)+\left(x-7\right) sifatida qaytadan yozish.

$$\left(x^{2}-7x\right)+\left(x-7\right)$$

x^{2}-7x ichida x ni ajrating.

$$x\left(x-7\right)+x-7$$

Distributiv funktsiyasidan foydalangan holda x-7 umumiy terminini chiqaring.

$$\left(x-7\right)\left(x+1\right)$$

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.

$$x^{2}-6x-7=0$$

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.

$$x=\frac{-\left(-6\right)±\sqrt{\left(-6\right)^{2}-4\left(-7\right)}}{2}$$

-6 kvadratini chiqarish.

$$x=\frac{-\left(-6\right)±\sqrt{36-4\left(-7\right)}}{2}$$

-4 ni -7 marotabaga ko'paytirish.

$$x=\frac{-\left(-6\right)±\sqrt{36+28}}{2}$$

36 ni 28 ga qo'shish.

$$x=\frac{-\left(-6\right)±\sqrt{64}}{2}$$

64 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-6\right)±8}{2}$$

-6 ning teskarisi 6 ga teng.

$$x=\frac{6±8}{2}$$

x=\frac{6±8}{2} tenglamasini yeching, bunda ± musbat. 6 ni 8 ga qo'shish.

$$x=\frac{14}{2}$$

14 ni 2 ga bo'lish.

$$x=7$$

x=\frac{6±8}{2} tenglamasini yeching, bunda ± manfiy. 6 dan 8 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 7 ga va x_{2} uchun -1 ga bo‘ling.

$$x^{2}-6x-7=\left(x-7\right)\left(x-\left(-1\right)\right)$$

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

$$x^{2}-6x-7=\left(x-7\right)\left(x+1\right)$$

Baholash

$$\left(x-7\right)\left(x+1\right)$$