k^2-4k-60 eching

$$k ^ { 2 } - 4 k - 60$$

Omil

$$\left(k-10\right)\left(k+6\right)$$

Yechim qadamlari

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

$$a+b=-4 ab=1\left(-60\right)=-60$$

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 – -4 yigʻindisini beruvchi juftlik.

$$a=-10 b=6$$

k^{2}-4k-60 ni \left(k^{2}-10k\right)+\left(6k-60\right) sifatida qaytadan yozish.

$$\left(k^{2}-10k\right)+\left(6k-60\right)$$

Birinchi guruhda k ni va ikkinchi guruhda 6 ni faktordan chiqaring.

$$k\left(k-10\right)+6\left(k-10\right)$$

Distributiv funktsiyasidan foydalangan holda k-10 umumiy terminini chiqaring.

$$\left(k-10\right)\left(k+6\right)$$

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.

$$k^{2}-4k-60=0$$

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.

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

-4 kvadratini chiqarish.

$$k=\frac{-\left(-4\right)±\sqrt{16-4\left(-60\right)}}{2}$$

-4 ni -60 marotabaga ko'paytirish.

$$k=\frac{-\left(-4\right)±\sqrt{16+240}}{2}$$

16 ni 240 ga qo'shish.

$$k=\frac{-\left(-4\right)±\sqrt{256}}{2}$$

256 ning kvadrat ildizini chiqarish.

$$k=\frac{-\left(-4\right)±16}{2}$$

-4 ning teskarisi 4 ga teng.

$$k=\frac{4±16}{2}$$

k=\frac{4±16}{2} tenglamasini yeching, bunda ± musbat. 4 ni 16 ga qo'shish.

$$k=\frac{20}{2}$$

20 ni 2 ga bo'lish.

$$k=10$$

k=\frac{4±16}{2} tenglamasini yeching, bunda ± manfiy. 4 dan 16 ni ayirish.

$$k=-\frac{12}{2}$$

-12 ni 2 ga bo'lish.

$$k=-6$$

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 -6 ga bo‘ling.

$$k^{2}-4k-60=\left(k-10\right)\left(k-\left(-6\right)\right)$$

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

$$k^{2}-4k-60=\left(k-10\right)\left(k+6\right)$$

Baholash

$$\left(k-10\right)\left(k+6\right)$$