5u^2-15u-50 eching

$$5 u ^ { 2 } - 15 u - 50$$

Omil

$$5\left(u-5\right)\left(u+2\right)$$

Yechim qadamlari

5 omili.

$$5\left(u^{2}-3u-10\right)$$

Hisoblang: u^{2}-3u-10. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda u^{2}+au+bu-10 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-3 ab=1\left(-10\right)=-10$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -10-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-10 2,-5$$

Har bir juftlik yigʻindisini hisoblang.

$$1-10=-9 2-5=-3$$

Yechim – -3 yigʻindisini beruvchi juftlik.

$$a=-5 b=2$$

u^{2}-3u-10 ni \left(u^{2}-5u\right)+\left(2u-10\right) sifatida qaytadan yozish.

$$\left(u^{2}-5u\right)+\left(2u-10\right)$$

Birinchi guruhda u ni va ikkinchi guruhda 2 ni faktordan chiqaring.

$$u\left(u-5\right)+2\left(u-5\right)$$

Distributiv funktsiyasidan foydalangan holda u-5 umumiy terminini chiqaring.

$$\left(u-5\right)\left(u+2\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$5\left(u-5\right)\left(u+2\right)$$

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.

$$5u^{2}-15u-50=0$$

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.

$$u=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}-4\times 5\left(-50\right)}}{2\times 5}$$

-15 kvadratini chiqarish.

$$u=\frac{-\left(-15\right)±\sqrt{225-4\times 5\left(-50\right)}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$u=\frac{-\left(-15\right)±\sqrt{225-20\left(-50\right)}}{2\times 5}$$

-20 ni -50 marotabaga ko'paytirish.

$$u=\frac{-\left(-15\right)±\sqrt{225+1000}}{2\times 5}$$

225 ni 1000 ga qo'shish.

$$u=\frac{-\left(-15\right)±\sqrt{1225}}{2\times 5}$$

1225 ning kvadrat ildizini chiqarish.

$$u=\frac{-\left(-15\right)±35}{2\times 5}$$

-15 ning teskarisi 15 ga teng.

$$u=\frac{15±35}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$u=\frac{15±35}{10}$$

u=\frac{15±35}{10} tenglamasini yeching, bunda ± musbat. 15 ni 35 ga qo'shish.

$$u=\frac{50}{10}$$

50 ni 10 ga bo'lish.

$$u=5$$

u=\frac{15±35}{10} tenglamasini yeching, bunda ± manfiy. 15 dan 35 ni ayirish.

$$u=-\frac{20}{10}$$

-20 ni 10 ga bo'lish.

$$u=-2$$

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

$$5u^{2}-15u-50=5\left(u-5\right)\left(u-\left(-2\right)\right)$$

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

$$5u^{2}-15u-50=5\left(u-5\right)\left(u+2\right)$$

Baholash

$$5\left(u-5\right)\left(u+2\right)$$