5x^2+17x+5 eching

$$5 x ^ { 2 } + 17 x + 5$$

Omil

$$5\left(x-\frac{-3\sqrt{21}-17}{10}\right)\left(x-\frac{3\sqrt{21}-17}{10}\right)$$

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.

$$5x^{2}+17x+5=0$$

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.

$$x=\frac{-17±\sqrt{17^{2}-4\times 5\times 5}}{2\times 5}$$

17 kvadratini chiqarish.

$$x=\frac{-17±\sqrt{289-4\times 5\times 5}}{2\times 5}$$

-4 ni 5 marotabaga ko'paytirish.

$$x=\frac{-17±\sqrt{289-20\times 5}}{2\times 5}$$

-20 ni 5 marotabaga ko'paytirish.

$$x=\frac{-17±\sqrt{289-100}}{2\times 5}$$

289 ni -100 ga qo'shish.

$$x=\frac{-17±\sqrt{189}}{2\times 5}$$

189 ning kvadrat ildizini chiqarish.

$$x=\frac{-17±3\sqrt{21}}{2\times 5}$$

2 ni 5 marotabaga ko'paytirish.

$$x=\frac{-17±3\sqrt{21}}{10}$$

x=\frac{-17±3\sqrt{21}}{10} tenglamasini yeching, bunda ± musbat. -17 ni 3\sqrt{21} ga qo'shish.

$$x=\frac{3\sqrt{21}-17}{10}$$

x=\frac{-17±3\sqrt{21}}{10} tenglamasini yeching, bunda ± manfiy. -17 dan 3\sqrt{21} ni ayirish.

$$x=\frac{-3\sqrt{21}-17}{10}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-17+3\sqrt{21}}{10} ga va x_{2} uchun \frac{-17-3\sqrt{21}}{10} ga bo‘ling.

$$5x^{2}+17x+5=5\left(x-\frac{3\sqrt{21}-17}{10}\right)\left(x-\frac{-3\sqrt{21}-17}{10}\right)$$

Baholash

$$5x^{2}+17x+5$$