4u^2-5u-6 eching

$$4 u ^ { 2 } - 5 u - 6$$

Omil

$$\left(u-2\right)\left(4u+3\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda 4u^{2}+au+bu-6 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-5 ab=4\left(-6\right)=-24$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -24-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-24 2,-12 3,-8 4,-6$$

Har bir juftlik yigʻindisini hisoblang.

$$1-24=-23 2-12=-10 3-8=-5 4-6=-2$$

Yechim – -5 yigʻindisini beruvchi juftlik.

$$a=-8 b=3$$

4u^{2}-5u-6 ni \left(4u^{2}-8u\right)+\left(3u-6\right) sifatida qaytadan yozish.

$$\left(4u^{2}-8u\right)+\left(3u-6\right)$$

Birinchi guruhda 4u ni va ikkinchi guruhda 3 ni faktordan chiqaring.

$$4u\left(u-2\right)+3\left(u-2\right)$$

Distributiv funktsiyasidan foydalangan holda u-2 umumiy terminini chiqaring.

$$\left(u-2\right)\left(4u+3\right)$$

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.

$$4u^{2}-5u-6=0$$

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.

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

-5 kvadratini chiqarish.

$$u=\frac{-\left(-5\right)±\sqrt{25-4\times 4\left(-6\right)}}{2\times 4}$$

-4 ni 4 marotabaga ko'paytirish.

$$u=\frac{-\left(-5\right)±\sqrt{25-16\left(-6\right)}}{2\times 4}$$

-16 ni -6 marotabaga ko'paytirish.

$$u=\frac{-\left(-5\right)±\sqrt{25+96}}{2\times 4}$$

25 ni 96 ga qo'shish.

$$u=\frac{-\left(-5\right)±\sqrt{121}}{2\times 4}$$

121 ning kvadrat ildizini chiqarish.

$$u=\frac{-\left(-5\right)±11}{2\times 4}$$

-5 ning teskarisi 5 ga teng.

$$u=\frac{5±11}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$u=\frac{5±11}{8}$$

u=\frac{5±11}{8} tenglamasini yeching, bunda ± musbat. 5 ni 11 ga qo'shish.

$$u=\frac{16}{8}$$

16 ni 8 ga bo'lish.

$$u=2$$

u=\frac{5±11}{8} tenglamasini yeching, bunda ± manfiy. 5 dan 11 ni ayirish.

$$u=-\frac{6}{8}$$

\frac{-6}{8} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$u=-\frac{3}{4}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 2 ga va x_{2} uchun -\frac{3}{4} ga bo‘ling.

$$4u^{2}-5u-6=4\left(u-2\right)\left(u-\left(-\frac{3}{4}\right)\right)$$

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

$$4u^{2}-5u-6=4\left(u-2\right)\left(u+\frac{3}{4}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{3}{4} ni u ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$4u^{2}-5u-6=4\left(u-2\right)\times \frac{4u+3}{4}$$

4 va 4 ichida eng katta umumiy 4 faktorini bekor qiling.

$$4u^{2}-5u-6=\left(u-2\right)\left(4u+3\right)$$

Baholash

$$\left(u-2\right)\left(4u+3\right)$$