-8r^2+26r-15 eching

$$- 8 r ^ { 2 } + 26 r - 15$$

Omil

$$\left(3-4r\right)\left(2r-5\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda -8r^{2}+ar+br-15 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=26 ab=-8\left(-15\right)=120$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b musbat boʻlganda, a va b ikkisi ham musbat. 120-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,120 2,60 3,40 4,30 5,24 6,20 8,15 10,12$$

Har bir juftlik yigʻindisini hisoblang.

$$1+120=121 2+60=62 3+40=43 4+30=34 5+24=29 6+20=26 8+15=23 10+12=22$$

Yechim – 26 yigʻindisini beruvchi juftlik.

$$a=20 b=6$$

-8r^{2}+26r-15 ni \left(-8r^{2}+20r\right)+\left(6r-15\right) sifatida qaytadan yozish.

$$\left(-8r^{2}+20r\right)+\left(6r-15\right)$$

Birinchi guruhda -4r ni va ikkinchi guruhda 3 ni faktordan chiqaring.

$$-4r\left(2r-5\right)+3\left(2r-5\right)$$

Distributiv funktsiyasidan foydalangan holda 2r-5 umumiy terminini chiqaring.

$$\left(2r-5\right)\left(-4r+3\right)$$

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.

$$-8r^{2}+26r-15=0$$

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.

$$r=\frac{-26±\sqrt{26^{2}-4\left(-8\right)\left(-15\right)}}{2\left(-8\right)}$$

26 kvadratini chiqarish.

$$r=\frac{-26±\sqrt{676-4\left(-8\right)\left(-15\right)}}{2\left(-8\right)}$$

-4 ni -8 marotabaga ko'paytirish.

$$r=\frac{-26±\sqrt{676+32\left(-15\right)}}{2\left(-8\right)}$$

32 ni -15 marotabaga ko'paytirish.

$$r=\frac{-26±\sqrt{676-480}}{2\left(-8\right)}$$

676 ni -480 ga qo'shish.

$$r=\frac{-26±\sqrt{196}}{2\left(-8\right)}$$

196 ning kvadrat ildizini chiqarish.

$$r=\frac{-26±14}{2\left(-8\right)}$$

2 ni -8 marotabaga ko'paytirish.

$$r=\frac{-26±14}{-16}$$

r=\frac{-26±14}{-16} tenglamasini yeching, bunda ± musbat. -26 ni 14 ga qo'shish.

$$r=-\frac{12}{-16}$$

\frac{-12}{-16} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$r=\frac{3}{4}$$

r=\frac{-26±14}{-16} tenglamasini yeching, bunda ± manfiy. -26 dan 14 ni ayirish.

$$r=-\frac{40}{-16}$$

\frac{-40}{-16} ulushini 8 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$r=\frac{5}{2}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{3}{4} ga va x_{2} uchun \frac{5}{2} ga bo‘ling.

$$-8r^{2}+26r-15=-8\left(r-\frac{3}{4}\right)\left(r-\frac{5}{2}\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{3}{4} ni r dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$-8r^{2}+26r-15=-8\times \frac{-4r+3}{-4}\left(r-\frac{5}{2}\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{5}{2} ni r dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$-8r^{2}+26r-15=-8\times \frac{-4r+3}{-4}\times \frac{-2r+5}{-2}$$

Raqamlash sonlarini va maxraj sonlariga ko'paytirish orqali \frac{-4r+3}{-4} ni \frac{-2r+5}{-2} ga ko'paytirish. So'ngra kasrni imkoni boricha eng kam a'zoga qisqartiring.

$$-8r^{2}+26r-15=-8\times \frac{\left(-4r+3\right)\left(-2r+5\right)}{-4\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$-8r^{2}+26r-15=-8\times \frac{\left(-4r+3\right)\left(-2r+5\right)}{8}$$

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

$$-8r^{2}+26r-15=-\left(-4r+3\right)\left(-2r+5\right)$$

Baholash

$$\left(3-4r\right)\left(2r-5\right)$$