3g^2-14g-5 eching

$$3 g ^ { 2 } - 14 g - 5$$

Omil

$$\left(g-5\right)\left(3g+1\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 3g^{2}+ag+bg-5 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-14 ab=3\left(-5\right)=-15$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -15-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-15 3,-5$$

Har bir juftlik yigʻindisini hisoblang.

$$1-15=-14 3-5=-2$$

Yechim – -14 yigʻindisini beruvchi juftlik.

$$a=-15 b=1$$

3g^{2}-14g-5 ni \left(3g^{2}-15g\right)+\left(g-5\right) sifatida qaytadan yozish.

$$\left(3g^{2}-15g\right)+\left(g-5\right)$$

3g^{2}-15g ichida 3g ni ajrating.

$$3g\left(g-5\right)+g-5$$

Distributiv funktsiyasidan foydalangan holda g-5 umumiy terminini chiqaring.

$$\left(g-5\right)\left(3g+1\right)$$

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.

$$3g^{2}-14g-5=0$$

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.

$$g=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}-4\times 3\left(-5\right)}}{2\times 3}$$

-14 kvadratini chiqarish.

$$g=\frac{-\left(-14\right)±\sqrt{196-4\times 3\left(-5\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$g=\frac{-\left(-14\right)±\sqrt{196-12\left(-5\right)}}{2\times 3}$$

-12 ni -5 marotabaga ko'paytirish.

$$g=\frac{-\left(-14\right)±\sqrt{196+60}}{2\times 3}$$

196 ni 60 ga qo'shish.

$$g=\frac{-\left(-14\right)±\sqrt{256}}{2\times 3}$$

256 ning kvadrat ildizini chiqarish.

$$g=\frac{-\left(-14\right)±16}{2\times 3}$$

-14 ning teskarisi 14 ga teng.

$$g=\frac{14±16}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$g=\frac{14±16}{6}$$

g=\frac{14±16}{6} tenglamasini yeching, bunda ± musbat. 14 ni 16 ga qo'shish.

$$g=\frac{30}{6}$$

30 ni 6 ga bo'lish.

$$g=5$$

g=\frac{14±16}{6} tenglamasini yeching, bunda ± manfiy. 14 dan 16 ni ayirish.

$$g=-\frac{2}{6}$$

\frac{-2}{6} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$g=-\frac{1}{3}$$

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

$$3g^{2}-14g-5=3\left(g-5\right)\left(g-\left(-\frac{1}{3}\right)\right)$$

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

$$3g^{2}-14g-5=3\left(g-5\right)\left(g+\frac{1}{3}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{1}{3} ni g ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$3g^{2}-14g-5=3\left(g-5\right)\times \frac{3g+1}{3}$$

3 va 3 ichida eng katta umumiy 3 faktorini bekor qiling.

$$3g^{2}-14g-5=\left(g-5\right)\left(3g+1\right)$$

Baholash

$$\left(g-5\right)\left(3g+1\right)$$