12-7x-10x^2 eching

$$12 - 7 x - 10 x ^ { 2 }$$

Omil

$$\left(4-5x\right)\left(2x+3\right)$$

Yechim qadamlari

Polinomni standart shaklga keltirish uchun uni qayta tartiblang. Shartlarni eng yuqoridan eng pastki qiymat ko'rsatgichiga joylashtirish.

$$-10x^{2}-7x+12$$

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda -10x^{2}+ax+bx+12 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-7 ab=-10\times 12=-120$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -120-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-120 2,-60 3,-40 4,-30 5,-24 6,-20 8,-15 10,-12$$

Har bir juftlik yigʻindisini hisoblang.

$$1-120=-119 2-60=-58 3-40=-37 4-30=-26 5-24=-19 6-20=-14 8-15=-7 10-12=-2$$

Yechim – -7 yigʻindisini beruvchi juftlik.

$$a=8 b=-15$$

-10x^{2}-7x+12 ni \left(-10x^{2}+8x\right)+\left(-15x+12\right) sifatida qaytadan yozish.

$$\left(-10x^{2}+8x\right)+\left(-15x+12\right)$$

Birinchi guruhda 2x ni va ikkinchi guruhda 3 ni faktordan chiqaring.

$$2x\left(-5x+4\right)+3\left(-5x+4\right)$$

Distributiv funktsiyasidan foydalangan holda -5x+4 umumiy terminini chiqaring.

$$\left(-5x+4\right)\left(2x+3\right)$$

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.

$$-10x^{2}-7x+12=0$$

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.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}-4\left(-10\right)\times 12}}{2\left(-10\right)}$$

-7 kvadratini chiqarish.

$$x=\frac{-\left(-7\right)±\sqrt{49-4\left(-10\right)\times 12}}{2\left(-10\right)}$$

-4 ni -10 marotabaga ko'paytirish.

$$x=\frac{-\left(-7\right)±\sqrt{49+40\times 12}}{2\left(-10\right)}$$

40 ni 12 marotabaga ko'paytirish.

$$x=\frac{-\left(-7\right)±\sqrt{49+480}}{2\left(-10\right)}$$

49 ni 480 ga qo'shish.

$$x=\frac{-\left(-7\right)±\sqrt{529}}{2\left(-10\right)}$$

529 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-7\right)±23}{2\left(-10\right)}$$

-7 ning teskarisi 7 ga teng.

$$x=\frac{7±23}{2\left(-10\right)}$$

2 ni -10 marotabaga ko'paytirish.

$$x=\frac{7±23}{-20}$$

x=\frac{7±23}{-20} tenglamasini yeching, bunda ± musbat. 7 ni 23 ga qo'shish.

$$x=\frac{30}{-20}$$

\frac{30}{-20} ulushini 10 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=-\frac{3}{2}$$

x=\frac{7±23}{-20} tenglamasini yeching, bunda ± manfiy. 7 dan 23 ni ayirish.

$$x=-\frac{16}{-20}$$

\frac{-16}{-20} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$x=\frac{4}{5}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -\frac{3}{2} ga va x_{2} uchun \frac{4}{5} ga bo‘ling.

$$-10x^{2}-7x+12=-10\left(x-\left(-\frac{3}{2}\right)\right)\left(x-\frac{4}{5}\right)$$

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

$$-10x^{2}-7x+12=-10\left(x+\frac{3}{2}\right)\left(x-\frac{4}{5}\right)$$

Umumiy maxrajni topib va hisoblovchini qo'shish orqali \frac{3}{2} ni x ga qo'shing. So'ngra agar imkoni bo'lsa kasrni eng kam shartga qisqartiring.

$$-10x^{2}-7x+12=-10\times \frac{-2x-3}{-2}\left(x-\frac{4}{5}\right)$$

Umumiy maxrajni topib va suratlarni ayirib \frac{4}{5} ni x dan ayirish. So'ngra imkoni boricha kasrni eng kichik shartga qisqartirish.

$$-10x^{2}-7x+12=-10\times \frac{-2x-3}{-2}\times \frac{-5x+4}{-5}$$

Raqamlash sonlarini va maxraj sonlariga ko'paytirish orqali \frac{-2x-3}{-2} ni \frac{-5x+4}{-5} ga ko'paytirish. So'ngra kasrni imkoni boricha eng kam a'zoga qisqartiring.

$$-10x^{2}-7x+12=-10\times \frac{\left(-2x-3\right)\left(-5x+4\right)}{-2\left(-5\right)}$$

-2 ni -5 marotabaga ko'paytirish.

$$-10x^{2}-7x+12=-10\times \frac{\left(-2x-3\right)\left(-5x+4\right)}{10}$$

-10 va 10 ichida eng katta umumiy 10 faktorini bekor qiling.

$$-10x^{2}-7x+12=-\left(-2x-3\right)\left(-5x+4\right)$$

Baholash

$$\left(4-5x\right)\left(2x+3\right)$$