2k^2-14k-60 eching

$$2 k ^ { 2 } - 14 k - 60$$

Omil

$$2\left(k-10\right)\left(k+3\right)$$

Yechim qadamlari

2 omili.

$$2\left(k^{2}-7k-30\right)$$

Hisoblang: k^{2}-7k-30. Ifodani guruhlash orqali faktorlang. Avvalo, ifoda k^{2}+ak+bk-30 sifatida qayta yozilishi kerak. a va b ni topish uchun yechiladigan tizimni sozlang.

$$a+b=-7 ab=1\left(-30\right)=-30$$

ab manfiy boʻlganda, a va b da qarama-qarshi belgilar bor. a+b manfiy boʻlganda, manfiy sonda musbatga nisbatdan kattaroq mutlaq qiymat bor. -30-mahsulotni beruvchi bunday butun juftliklarni roʻyxat qiling.

$$1,-30 2,-15 3,-10 5,-6$$

Har bir juftlik yigʻindisini hisoblang.

$$1-30=-29 2-15=-13 3-10=-7 5-6=-1$$

Yechim – -7 yigʻindisini beruvchi juftlik.

$$a=-10 b=3$$

k^{2}-7k-30 ni \left(k^{2}-10k\right)+\left(3k-30\right) sifatida qaytadan yozish.

$$\left(k^{2}-10k\right)+\left(3k-30\right)$$

Birinchi guruhda k ni va ikkinchi guruhda 3 ni faktordan chiqaring.

$$k\left(k-10\right)+3\left(k-10\right)$$

Distributiv funktsiyasidan foydalangan holda k-10 umumiy terminini chiqaring.

$$\left(k-10\right)\left(k+3\right)$$

Toʻliq ajratilgan ifodani qaytadan yozing.

$$2\left(k-10\right)\left(k+3\right)$$

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.

$$2k^{2}-14k-60=0$$

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.

$$k=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}-4\times 2\left(-60\right)}}{2\times 2}$$

-14 kvadratini chiqarish.

$$k=\frac{-\left(-14\right)±\sqrt{196-4\times 2\left(-60\right)}}{2\times 2}$$

-4 ni 2 marotabaga ko'paytirish.

$$k=\frac{-\left(-14\right)±\sqrt{196-8\left(-60\right)}}{2\times 2}$$

-8 ni -60 marotabaga ko'paytirish.

$$k=\frac{-\left(-14\right)±\sqrt{196+480}}{2\times 2}$$

196 ni 480 ga qo'shish.

$$k=\frac{-\left(-14\right)±\sqrt{676}}{2\times 2}$$

676 ning kvadrat ildizini chiqarish.

$$k=\frac{-\left(-14\right)±26}{2\times 2}$$

-14 ning teskarisi 14 ga teng.

$$k=\frac{14±26}{2\times 2}$$

2 ni 2 marotabaga ko'paytirish.

$$k=\frac{14±26}{4}$$

k=\frac{14±26}{4} tenglamasini yeching, bunda ± musbat. 14 ni 26 ga qo'shish.

$$k=\frac{40}{4}$$

40 ni 4 ga bo'lish.

$$k=10$$

k=\frac{14±26}{4} tenglamasini yeching, bunda ± manfiy. 14 dan 26 ni ayirish.

$$k=-\frac{12}{4}$$

-12 ni 4 ga bo'lish.

$$k=-3$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 10 ga va x_{2} uchun -3 ga bo‘ling.

$$2k^{2}-14k-60=2\left(k-10\right)\left(k-\left(-3\right)\right)$$

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

$$2k^{2}-14k-60=2\left(k-10\right)\left(k+3\right)$$

Baholash

$$2\left(k-10\right)\left(k+3\right)$$