2d^2-9d-11 eching

$$2 d ^ { 2 } - 9 d - 11$$

Omil

$$\left(2d-11\right)\left(d+1\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 2d^{2}+ad+bd-11 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-9 ab=2\left(-11\right)=-22$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -22-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-22 2,-11$$

Har bir juftlik yigʻindisini hisoblang.

$$1-22=-21 2-11=-9$$

Yechim – -9 yigʻindisini beruvchi juftlik.

$$a=-11 b=2$$

2d^{2}-9d-11 ni \left(2d^{2}-11d\right)+\left(2d-11\right) sifatida qaytadan yozish.

$$\left(2d^{2}-11d\right)+\left(2d-11\right)$$

2d^{2}-11d ichida d ni ajrating.

$$d\left(2d-11\right)+2d-11$$

Distributiv funktsiyasidan foydalangan holda 2d-11 umumiy terminini chiqaring.

$$\left(2d-11\right)\left(d+1\right)$$

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.

$$2d^{2}-9d-11=0$$

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.

$$d=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 2\left(-11\right)}}{2\times 2}$$

-9 kvadratini chiqarish.

$$d=\frac{-\left(-9\right)±\sqrt{81-4\times 2\left(-11\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$d=\frac{-\left(-9\right)±\sqrt{81-8\left(-11\right)}}{2\times 2}$$

-8 ni -11 marotabaga ko'paytirish.

$$d=\frac{-\left(-9\right)±\sqrt{81+88}}{2\times 2}$$

81 ni 88 ga qo'shish.

$$d=\frac{-\left(-9\right)±\sqrt{169}}{2\times 2}$$

169 ning kvadrat ildizini chiqarish.

$$d=\frac{-\left(-9\right)±13}{2\times 2}$$

-9 ning teskarisi 9 ga teng.

$$d=\frac{9±13}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$d=\frac{9±13}{4}$$

d=\frac{9±13}{4} tenglamasini yeching, bunda ± musbat. 9 ni 13 ga qo'shish.

$$d=\frac{22}{4}$$

\frac{22}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$d=\frac{11}{2}$$

d=\frac{9±13}{4} tenglamasini yeching, bunda ± manfiy. 9 dan 13 ni ayirish.

$$d=-\frac{4}{4}$$

-4 ni 4 ga bo'lish.

$$d=-1$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{11}{2} ga va x_{2} uchun -1 ga bo‘ling.

$$2d^{2}-9d-11=2\left(d-\frac{11}{2}\right)\left(d-\left(-1\right)\right)$$

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

$$2d^{2}-9d-11=2\left(d-\frac{11}{2}\right)\left(d+1\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{11}{2} ni d dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$2d^{2}-9d-11=2\times \frac{2d-11}{2}\left(d+1\right)$$

2 va 2 ichida eng katta umumiy 2 faktorini bekor qiling.

$$2d^{2}-9d-11=\left(2d-11\right)\left(d+1\right)$$

Baholash

$$\left(2d-11\right)\left(d+1\right)$$