g(p)=-60p^2+50p+10 eching

$$g ( p ) = - 60 p ^ { 2 } + 50 p + 10$$

Omil

$$10\left(1-p\right)\left(6p+1\right)$$

Yechim qadamlari

10 omili.

$$10\left(-6p^{2}+5p+1\right)$$

Hisoblang: -6p^{2}+5p+1. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda -6p^{2}+ap+bp+1 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=5 ab=-6=-6$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b musbat boʻlganda, musbat sonda manfiyga nisbatdan kattaroq mutlaq qiymat bor. -6-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$-1,6 -2,3$$

Har bir juftlik yigʻindisini hisoblang.

$$-1+6=5 -2+3=1$$

Yechim – 5 yigʻindisini beruvchi juftlik.

$$a=6 b=-1$$

-6p^{2}+5p+1 ni \left(-6p^{2}+6p\right)+\left(-p+1\right) sifatida qaytadan yozish.

$$\left(-6p^{2}+6p\right)+\left(-p+1\right)$$

-6p^{2}+6p ichida 6p ni ajrating.

$$6p\left(-p+1\right)-p+1$$

Distributiv funktsiyasidan foydalangan holda -p+1 umumiy terminini chiqaring.

$$\left(-p+1\right)\left(6p+1\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$10\left(-p+1\right)\left(6p+1\right)$$

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.

$$-60p^{2}+50p+10=0$$

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.

$$p=\frac{-50±\sqrt{50^{2}-4\left(-60\right)\times 10}}{2\left(-60\right)}$$

50 kvadratini chiqarish.

$$p=\frac{-50±\sqrt{2500-4\left(-60\right)\times 10}}{2\left(-60\right)}$$

-4 ni -60 marotabaga ko'paytirish.

$$p=\frac{-50±\sqrt{2500+240\times 10}}{2\left(-60\right)}$$

240 ni 10 marotabaga ko'paytirish.

$$p=\frac{-50±\sqrt{2500+2400}}{2\left(-60\right)}$$

2500 ni 2400 ga qo'shish.

$$p=\frac{-50±\sqrt{4900}}{2\left(-60\right)}$$

4900 ning kvadrat ildizini chiqarish.

$$p=\frac{-50±70}{2\left(-60\right)}$$

2 ni -60 marotabaga ko'paytirish.

$$p=\frac{-50±70}{-120}$$

p=\frac{-50±70}{-120} tenglamasini yeching, bunda ± musbat. -50 ni 70 ga qo'shish.

$$p=\frac{20}{-120}$$

\frac{20}{-120} ulushini 20 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$p=-\frac{1}{6}$$

p=\frac{-50±70}{-120} tenglamasini yeching, bunda ± manfiy. -50 dan 70 ni ayirish.

$$p=-\frac{120}{-120}$$

-120 ni -120 ga bo'lish.

$$p=1$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -\frac{1}{6} ga va x_{2} uchun 1 ga bo‘ling.

$$-60p^{2}+50p+10=-60\left(p-\left(-\frac{1}{6}\right)\right)\left(p-1\right)$$

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

$$-60p^{2}+50p+10=-60\left(p+\frac{1}{6}\right)\left(p-1\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{6} ni p ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$-60p^{2}+50p+10=-60\times \frac{-6p-1}{-6}\left(p-1\right)$$

-60 va 6 ichida eng katta umumiy 6 faktorini bekor qiling.

$$-60p^{2}+50p+10=10\left(-6p-1\right)\left(p-1\right)$$

Baholash

$$10+50p-60p^{2}$$