y(x)=4x^2+2x-3 eching

$$y ( x ) = 4 x ^ { 2 } + 2 x - 3$$

Omil

$$4\left(x-\frac{-\sqrt{13}-1}{4}\right)\left(x-\frac{\sqrt{13}-1}{4}\right)$$

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.

$$4x^{2}+2x-3=0$$

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.

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

2 kvadratini chiqarish.

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

-4 ni 4 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4-16\left(-3\right)}}{2\times 4}$$

-16 ni -3 marotabaga ko'paytirish.

$$x=\frac{-2±\sqrt{4+48}}{2\times 4}$$

4 ni 48 ga qo'shish.

$$x=\frac{-2±\sqrt{52}}{2\times 4}$$

52 ning kvadrat ildizini chiqarish.

$$x=\frac{-2±2\sqrt{13}}{2\times 4}$$

2 ni 4 marotabaga ko'paytirish.

$$x=\frac{-2±2\sqrt{13}}{8}$$

x=\frac{-2±2\sqrt{13}}{8} tenglamasini yeching, bunda ± musbat. -2 ni 2\sqrt{13} ga qo'shish.

$$x=\frac{2\sqrt{13}-2}{8}$$

-2+2\sqrt{13} ni 8 ga bo'lish.

$$x=\frac{\sqrt{13}-1}{4}$$

x=\frac{-2±2\sqrt{13}}{8} tenglamasini yeching, bunda ± manfiy. -2 dan 2\sqrt{13} ni ayirish.

$$x=\frac{-2\sqrt{13}-2}{8}$$

-2-2\sqrt{13} ni 8 ga bo'lish.

$$x=\frac{-\sqrt{13}-1}{4}$$

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{13}}{4} ga va x_{2} uchun \frac{-1-\sqrt{13}}{4} ga bo‘ling.

$$4x^{2}+2x-3=4\left(x-\frac{\sqrt{13}-1}{4}\right)\left(x-\frac{-\sqrt{13}-1}{4}\right)$$

Baholash

$$4x^{2}+2x-3$$