x^2-11x-60= eching

$$x ^ { 2 } - 11 x - 60 =$$

Omil

$$\left(x-15\right)\left(x+4\right)$$

Yechim qadamlari

Ifodani guruhlash orqali faktorlang. Avvalo, ifoda x^{2}+ax+bx-60 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-11 ab=1\left(-60\right)=-60$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -60-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-60 2,-30 3,-20 4,-15 5,-12 6,-10$$

Har bir juftlik yigʻindisini hisoblang.

$$1-60=-59 2-30=-28 3-20=-17 4-15=-11 5-12=-7 6-10=-4$$

Yechim – -11 yigʻindisini beruvchi juftlik.

$$a=-15 b=4$$

x^{2}-11x-60 ni \left(x^{2}-15x\right)+\left(4x-60\right) sifatida qaytadan yozish.

$$\left(x^{2}-15x\right)+\left(4x-60\right)$$

Birinchi guruhda x ni va ikkinchi guruhda 4 ni faktordan chiqaring.

$$x\left(x-15\right)+4\left(x-15\right)$$

Distributiv funktsiyasidan foydalangan holda x-15 umumiy terminini chiqaring.

$$\left(x-15\right)\left(x+4\right)$$

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.

$$x^{2}-11x-60=0$$

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.

$$x=\frac{-\left(-11\right)±\sqrt{\left(-11\right)^{2}-4\left(-60\right)}}{2}$$

-11 kvadratini chiqarish.

$$x=\frac{-\left(-11\right)±\sqrt{121-4\left(-60\right)}}{2}$$

-4 ni -60 marotabaga ko'paytirish.

$$x=\frac{-\left(-11\right)±\sqrt{121+240}}{2}$$

121 ni 240 ga qo'shish.

$$x=\frac{-\left(-11\right)±\sqrt{361}}{2}$$

361 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-11\right)±19}{2}$$

-11 ning teskarisi 11 ga teng.

$$x=\frac{11±19}{2}$$

x=\frac{11±19}{2} tenglamasini yeching, bunda ± musbat. 11 ni 19 ga qo'shish.

$$x=\frac{30}{2}$$

30 ni 2 ga bo'lish.

$$x=15$$

x=\frac{11±19}{2} tenglamasini yeching, bunda ± manfiy. 11 dan 19 ni ayirish.

$$x=-\frac{8}{2}$$

-8 ni 2 ga bo'lish.

$$x=-4$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 15 ga va x_{2} uchun -4 ga bo‘ling.

$$x^{2}-11x-60=\left(x-15\right)\left(x-\left(-4\right)\right)$$

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

$$x^{2}-11x-60=\left(x-15\right)\left(x+4\right)$$

Baholash

$$\left(x-15\right)\left(x+4\right)$$