5w^2+13w-6 eching

$$5 w ^ { 2 } + 13 w - 6$$

Omil

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

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 5w^{2}+aw+bw-6 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=13 ab=5\left(-6\right)=-30$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b musbat boʻlganda, musbat sonda manfiyga nisbatdan kattaroq mutlaq qiymat bor. -30-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$-1,30 -2,15 -3,10 -5,6$$

Har bir juftlik yigʻindisini hisoblang.

$$-1+30=29 -2+15=13 -3+10=7 -5+6=1$$

Yechim – 13 yigʻindisini beruvchi juftlik.

$$a=-2 b=15$$

5w^{2}+13w-6 ni \left(5w^{2}-2w\right)+\left(15w-6\right) sifatida qaytadan yozish.

$$\left(5w^{2}-2w\right)+\left(15w-6\right)$$

Birinchi guruhda w ni va ikkinchi guruhda 3 ni faktordan chiqaring.

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

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

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

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.

$$5w^{2}+13w-6=0$$

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.

$$w=\frac{-13±\sqrt{13^{2}-4\times 5\left(-6\right)}}{2\times 5}$$

13 kvadratini chiqarish.

$$w=\frac{-13±\sqrt{169-4\times 5\left(-6\right)}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$w=\frac{-13±\sqrt{169-20\left(-6\right)}}{2\times 5}$$

-20 ni -6 marotabaga ko'paytirish.

$$w=\frac{-13±\sqrt{169+120}}{2\times 5}$$

169 ni 120 ga qo'shish.

$$w=\frac{-13±\sqrt{289}}{2\times 5}$$

289 ning kvadrat ildizini chiqarish.

$$w=\frac{-13±17}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$w=\frac{-13±17}{10}$$

w=\frac{-13±17}{10} tenglamasini yeching, bunda ± musbat. -13 ni 17 ga qo'shish.

$$w=\frac{4}{10}$$

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

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

w=\frac{-13±17}{10} tenglamasini yeching, bunda ± manfiy. -13 dan 17 ni ayirish.

$$w=-\frac{30}{10}$$

-30 ni 10 ga bo'lish.

$$w=-3$$

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

$$5w^{2}+13w-6=5\left(w-\frac{2}{5}\right)\left(w-\left(-3\right)\right)$$

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

$$5w^{2}+13w-6=5\left(w-\frac{2}{5}\right)\left(w+3\right)$$

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

$$5w^{2}+13w-6=5\times \frac{5w-2}{5}\left(w+3\right)$$

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

$$5w^{2}+13w-6=\left(5w-2\right)\left(w+3\right)$$

Baholash

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