-3x^2-4x-1 eching

$$-3 { x }^{ 2 } -4x-1$$

Omil

$$-\left(x+1\right)\left(3x+1\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda -3x^{2}+ax+bx-1 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-4 ab=-3\left(-1\right)=3$$

ab musbat boʻlganda, a va b da bir xil belgi bor. a+b manfiy boʻlganda, a va b ikkisi ham manfiy. Faqat bundan juftlik tizim yechimidir.

$$a=-1 b=-3$$

-3x^{2}-4x-1 ni \left(-3x^{2}-x\right)+\left(-3x-1\right) sifatida qaytadan yozish.

$$\left(-3x^{2}-x\right)+\left(-3x-1\right)$$

Birinchi guruhda -x ni va ikkinchi guruhda -1 ni faktordan chiqaring.

$$-x\left(3x+1\right)-\left(3x+1\right)$$

Distributiv funktsiyasidan foydalangan holda 3x+1 umumiy terminini chiqaring.

$$\left(3x+1\right)\left(-x-1\right)$$

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.

$$-3x^{2}-4x-1=0$$

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.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-3\right)\left(-1\right)}}{2\left(-3\right)}$$

-4 kvadratini chiqarish.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\left(-3\right)\left(-1\right)}}{2\left(-3\right)}$$

-4 ni -3 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16+12\left(-1\right)}}{2\left(-3\right)}$$

12 ni -1 marotabaga ko'paytirish.

$$x=\frac{-\left(-4\right)±\sqrt{16-12}}{2\left(-3\right)}$$

16 ni -12 ga qo'shish.

$$x=\frac{-\left(-4\right)±\sqrt{4}}{2\left(-3\right)}$$

4 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-4\right)±2}{2\left(-3\right)}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±2}{2\left(-3\right)}$$

2 ni -3 marotabaga ko'paytirish.

$$x=\frac{4±2}{-6}$$

x=\frac{4±2}{-6} tenglamasini yeching, bunda ± musbat. 4 ni 2 ga qo'shish.

$$x=\frac{6}{-6}$$

6 ni -6 ga bo'lish.

$$x=-1$$

x=\frac{4±2}{-6} tenglamasini yeching, bunda ± manfiy. 4 dan 2 ni ayirish.

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

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

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

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

$$-3x^{2}-4x-1=-3\left(x-\left(-1\right)\right)\left(x-\left(-\frac{1}{3}\right)\right)$$

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

$$-3x^{2}-4x-1=-3\left(x+1\right)\left(x+\frac{1}{3}\right)$$

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

$$-3x^{2}-4x-1=-3\left(x+1\right)\times \frac{-3x-1}{-3}$$

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

$$-3x^{2}-4x-1=\left(x+1\right)\left(-3x-1\right)$$

Baholash

$$-\left(x+1\right)\left(3x+1\right)$$