4x^2-3x-7 eching

$$4 { x }^{ 2 } -3x-7$$

Omil

$$\left(4x-7\right)\left(x+1\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 4x^{2}+ax+bx-7 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-3 ab=4\left(-7\right)=-28$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -28-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-28 2,-14 4,-7$$

Har bir juftlik yigʻindisini hisoblang.

$$1-28=-27 2-14=-12 4-7=-3$$

Yechim – -3 yigʻindisini beruvchi juftlik.

$$a=-7 b=4$$

4x^{2}-3x-7 ni \left(4x^{2}-7x\right)+\left(4x-7\right) sifatida qaytadan yozish.

$$\left(4x^{2}-7x\right)+\left(4x-7\right)$$

4x^{2}-7x ichida x ni ajrating.

$$x\left(4x-7\right)+4x-7$$

Distributiv funktsiyasidan foydalangan holda 4x-7 umumiy terminini chiqaring.

$$\left(4x-7\right)\left(x+1\right)$$

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.

$$4x^{2}-3x-7=0$$

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.

$$x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 4\left(-7\right)}}{2\times 4}$$

-3 kvadratini chiqarish.

$$x=\frac{-\left(-3\right)±\sqrt{9-4\times 4\left(-7\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9-16\left(-7\right)}}{2\times 4}$$

-16 ni -7 marotabaga ko'paytirish.

$$x=\frac{-\left(-3\right)±\sqrt{9+112}}{2\times 4}$$

9 ni 112 ga qo'shish.

$$x=\frac{-\left(-3\right)±\sqrt{121}}{2\times 4}$$

121 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-3\right)±11}{2\times 4}$$

-3 ning teskarisi 3 ga teng.

$$x=\frac{3±11}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{3±11}{8}$$

x=\frac{3±11}{8} tenglamasini yeching, bunda ± musbat. 3 ni 11 ga qo'shish.

$$x=\frac{14}{8}$$

\frac{14}{8} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{7}{4}$$

x=\frac{3±11}{8} tenglamasini yeching, bunda ± manfiy. 3 dan 11 ni ayirish.

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

-8 ni 8 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 \frac{7}{4} ga va x_{2} uchun -1 ga bo‘ling.

$$4x^{2}-3x-7=4\left(x-\frac{7}{4}\right)\left(x-\left(-1\right)\right)$$

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

$$4x^{2}-3x-7=4\left(x-\frac{7}{4}\right)\left(x+1\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{7}{4} ni x dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$4x^{2}-3x-7=4\times \frac{4x-7}{4}\left(x+1\right)$$

4 va 4 ichida eng katta umumiy 4 faktorini bekor qiling.

$$4x^{2}-3x-7=\left(4x-7\right)\left(x+1\right)$$

Baholash

$$\left(4x-7\right)\left(x+1\right)$$