3x^2+2x-10 eching

$$3 x ^ { 2 } + 2 x - 10$$

Omil

$$3\left(x-\frac{-\sqrt{31}-1}{3}\right)\left(x-\frac{\sqrt{31}-1}{3}\right)$$

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.

$$3x^{2}+2x-10=0$$

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.

$$x=\frac{-2±\sqrt{2^{2}-4\times 3\left(-10\right)}}{2\times 3}$$

2 kvadratini chiqarish.

$$x=\frac{-2±\sqrt{4-4\times 3\left(-10\right)}}{2\times 3}$$

-4 ni 3 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4-12\left(-10\right)}}{2\times 3}$$

-12 ni -10 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4+120}}{2\times 3}$$

4 ni 120 ga qo'shish.

$$x=\frac{-2±\sqrt{124}}{2\times 3}$$

124 ning kvadrat ildizini chiqarish.

$$x=\frac{-2±2\sqrt{31}}{2\times 3}$$

2 ni 3 marotabaga ko'paytirish.

$$x=\frac{-2±2\sqrt{31}}{6}$$

x=\frac{-2±2\sqrt{31}}{6} tenglamasini yeching, bunda ± musbat. -2 ni 2\sqrt{31} ga qo'shish.

$$x=\frac{2\sqrt{31}-2}{6}$$

-2+2\sqrt{31} ni 6 ga bo'lish.

$$x=\frac{\sqrt{31}-1}{3}$$

x=\frac{-2±2\sqrt{31}}{6} tenglamasini yeching, bunda ± manfiy. -2 dan 2\sqrt{31} ni ayirish.

$$x=\frac{-2\sqrt{31}-2}{6}$$

-2-2\sqrt{31} ni 6 ga bo'lish.

$$x=\frac{-\sqrt{31}-1}{3}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-1+\sqrt{31}}{3} ga va x_{2} uchun \frac{-1-\sqrt{31}}{3} ga bo‘ling.

$$3x^{2}+2x-10=3\left(x-\frac{\sqrt{31}-1}{3}\right)\left(x-\frac{-\sqrt{31}-1}{3}\right)$$

Baholash

$$3x^{2}+2x-10$$