10s^2+19s-15 eching

$$10 s ^ { 2 } + 19 s - 15$$

Omil

$$\left(5s-3\right)\left(2s+5\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 10s^{2}+as+bs-15 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=19 ab=10\left(-15\right)=-150$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b musbat boʻlganda, musbat sonda manfiyga nisbatdan kattaroq mutlaq qiymat bor. -150-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$-1,150 -2,75 -3,50 -5,30 -6,25 -10,15$$

Har bir juftlik yigʻindisini hisoblang.

$$-1+150=149 -2+75=73 -3+50=47 -5+30=25 -6+25=19 -10+15=5$$

Yechim – 19 yigʻindisini beruvchi juftlik.

$$a=-6 b=25$$

10s^{2}+19s-15 ni \left(10s^{2}-6s\right)+\left(25s-15\right) sifatida qaytadan yozish.

$$\left(10s^{2}-6s\right)+\left(25s-15\right)$$

Birinchi guruhda 2s ni va ikkinchi guruhda 5 ni faktordan chiqaring.

$$2s\left(5s-3\right)+5\left(5s-3\right)$$

Distributiv funktsiyasidan foydalangan holda 5s-3 umumiy terminini chiqaring.

$$\left(5s-3\right)\left(2s+5\right)$$

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.

$$10s^{2}+19s-15=0$$

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.

$$s=\frac{-19±\sqrt{19^{2}-4\times 10\left(-15\right)}}{2\times 10}$$

19 kvadratini chiqarish.

$$s=\frac{-19±\sqrt{361-4\times 10\left(-15\right)}}{2\times 10}$$

-4 ni 10 marotabaga ko'paytirish.

$$s=\frac{-19±\sqrt{361-40\left(-15\right)}}{2\times 10}$$

-40 ni -15 marotabaga ko'paytirish.

$$s=\frac{-19±\sqrt{361+600}}{2\times 10}$$

361 ni 600 ga qo'shish.

$$s=\frac{-19±\sqrt{961}}{2\times 10}$$

961 ning kvadrat ildizini chiqarish.

$$s=\frac{-19±31}{2\times 10}$$

2 ni 10 marotabaga ko'paytirish.

$$s=\frac{-19±31}{20}$$

s=\frac{-19±31}{20} tenglamasini yeching, bunda ± musbat. -19 ni 31 ga qo'shish.

$$s=\frac{12}{20}$$

\frac{12}{20} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$s=\frac{3}{5}$$

s=\frac{-19±31}{20} tenglamasini yeching, bunda ± manfiy. -19 dan 31 ni ayirish.

$$s=-\frac{50}{20}$$

\frac{-50}{20} ulushini 10 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$s=-\frac{5}{2}$$

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

$$10s^{2}+19s-15=10\left(s-\frac{3}{5}\right)\left(s-\left(-\frac{5}{2}\right)\right)$$

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

$$10s^{2}+19s-15=10\left(s-\frac{3}{5}\right)\left(s+\frac{5}{2}\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{3}{5} ni s dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$10s^{2}+19s-15=10\times \frac{5s-3}{5}\left(s+\frac{5}{2}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{5}{2} ni s ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$10s^{2}+19s-15=10\times \frac{5s-3}{5}\times \frac{2s+5}{2}$$

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

$$10s^{2}+19s-15=10\times \frac{\left(5s-3\right)\left(2s+5\right)}{5\times 2}$$

5 ni 2 marotabaga ko'paytirish.

$$10s^{2}+19s-15=10\times \frac{\left(5s-3\right)\left(2s+5\right)}{10}$$

10 va 10 ichida eng katta umumiy 10 faktorini bekor qiling.

$$10s^{2}+19s-15=\left(5s-3\right)\left(2s+5\right)$$

Baholash

$$\left(5s-3\right)\left(2s+5\right)$$