5p^2-48p-20 eching

$$5 p ^ { 2 } - 48 p - 20$$

Omil

$$\left(p-10\right)\left(5p+2\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 5p^{2}+ap+bp-20 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-48 ab=5\left(-20\right)=-100$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -100-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-100 2,-50 4,-25 5,-20 10,-10$$

Har bir juftlik yigʻindisini hisoblang.

$$1-100=-99 2-50=-48 4-25=-21 5-20=-15 10-10=0$$

Yechim – -48 yigʻindisini beruvchi juftlik.

$$a=-50 b=2$$

5p^{2}-48p-20 ni \left(5p^{2}-50p\right)+\left(2p-20\right) sifatida qaytadan yozish.

$$\left(5p^{2}-50p\right)+\left(2p-20\right)$$

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

$$5p\left(p-10\right)+2\left(p-10\right)$$

Distributiv funktsiyasidan foydalangan holda p-10 umumiy terminini chiqaring.

$$\left(p-10\right)\left(5p+2\right)$$

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.

$$5p^{2}-48p-20=0$$

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.

$$p=\frac{-\left(-48\right)±\sqrt{\left(-48\right)^{2}-4\times 5\left(-20\right)}}{2\times 5}$$

-48 kvadratini chiqarish.

$$p=\frac{-\left(-48\right)±\sqrt{2304-4\times 5\left(-20\right)}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$p=\frac{-\left(-48\right)±\sqrt{2304-20\left(-20\right)}}{2\times 5}$$

-20 ni -20 marotabaga ko'paytirish.

$$p=\frac{-\left(-48\right)±\sqrt{2304+400}}{2\times 5}$$

2304 ni 400 ga qo'shish.

$$p=\frac{-\left(-48\right)±\sqrt{2704}}{2\times 5}$$

2704 ning kvadrat ildizini chiqarish.

$$p=\frac{-\left(-48\right)±52}{2\times 5}$$

-48 ning teskarisi 48 ga teng.

$$p=\frac{48±52}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$p=\frac{48±52}{10}$$

p=\frac{48±52}{10} tenglamasini yeching, bunda ± musbat. 48 ni 52 ga qo'shish.

$$p=\frac{100}{10}$$

100 ni 10 ga bo'lish.

$$p=10$$

p=\frac{48±52}{10} tenglamasini yeching, bunda ± manfiy. 48 dan 52 ni ayirish.

$$p=-\frac{4}{10}$$

\frac{-4}{10} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 10 ga va x_{2} uchun -\frac{2}{5} ga bo‘ling.

$$5p^{2}-48p-20=5\left(p-10\right)\left(p-\left(-\frac{2}{5}\right)\right)$$

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

$$5p^{2}-48p-20=5\left(p-10\right)\left(p+\frac{2}{5}\right)$$

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

$$5p^{2}-48p-20=5\left(p-10\right)\times \frac{5p+2}{5}$$

5 va 5 ichida eng katta umumiy 5 faktorini bekor qiling.

$$5p^{2}-48p-20=\left(p-10\right)\left(5p+2\right)$$

Baholash

$$\left(p-10\right)\left(5p+2\right)$$