-8x^2-15x+2 eching

$$- 8 x ^ { 2 } - 15 x + 2$$

Omil

$$-\left(8x-1\right)\left(x+2\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda -8x^{2}+ax+bx+2 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-15 ab=-8\times 2=-16$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -16-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-16 2,-8 4,-4$$

Har bir juftlik yigʻindisini hisoblang.

$$1-16=-15 2-8=-6 4-4=0$$

Yechim – -15 yigʻindisini beruvchi juftlik.

$$a=1 b=-16$$

-8x^{2}-15x+2 ni \left(-8x^{2}+x\right)+\left(-16x+2\right) sifatida qaytadan yozish.

$$\left(-8x^{2}+x\right)+\left(-16x+2\right)$$

Birinchi guruhda -x ni va ikkinchi guruhda -2 ni faktordan chiqaring.

$$-x\left(8x-1\right)-2\left(8x-1\right)$$

Distributiv funktsiyasidan foydalangan holda 8x-1 umumiy terminini chiqaring.

$$\left(8x-1\right)\left(-x-2\right)$$

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.

$$-8x^{2}-15x+2=0$$

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.

$$x=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}-4\left(-8\right)\times 2}}{2\left(-8\right)}$$

-15 kvadratini chiqarish.

$$x=\frac{-\left(-15\right)±\sqrt{225-4\left(-8\right)\times 2}}{2\left(-8\right)}$$

-4 ni -8 marotabaga ko'paytirish.

$$x=\frac{-\left(-15\right)±\sqrt{225+32\times 2}}{2\left(-8\right)}$$

32 ni 2 marotabaga ko'paytirish.

$$x=\frac{-\left(-15\right)±\sqrt{225+64}}{2\left(-8\right)}$$

225 ni 64 ga qo'shish.

$$x=\frac{-\left(-15\right)±\sqrt{289}}{2\left(-8\right)}$$

289 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-15\right)±17}{2\left(-8\right)}$$

-15 ning teskarisi 15 ga teng.

$$x=\frac{15±17}{2\left(-8\right)}$$

2 ni -8 marotabaga ko'paytirish.

$$x=\frac{15±17}{-16}$$

x=\frac{15±17}{-16} tenglamasini yeching, bunda ± musbat. 15 ni 17 ga qo'shish.

$$x=\frac{32}{-16}$$

32 ni -16 ga bo'lish.

$$x=-2$$

x=\frac{15±17}{-16} tenglamasini yeching, bunda ± manfiy. 15 dan 17 ni ayirish.

$$x=-\frac{2}{-16}$$

\frac{-2}{-16} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{1}{8}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -2 ga va x_{2} uchun \frac{1}{8} ga bo‘ling.

$$-8x^{2}-15x+2=-8\left(x-\left(-2\right)\right)\left(x-\frac{1}{8}\right)$$

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

$$-8x^{2}-15x+2=-8\left(x+2\right)\left(x-\frac{1}{8}\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{1}{8} ni x dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$-8x^{2}-15x+2=-8\left(x+2\right)\times \frac{-8x+1}{-8}$$

-8 va 8 ichida eng katta umumiy 8 faktorini bekor qiling.

$$-8x^{2}-15x+2=\left(x+2\right)\left(-8x+1\right)$$

Baholash

$$-\left(8x-1\right)\left(x+2\right)$$