f(x)=x^2-4x-15 eching

$$f ( x ) = x ^ { 2 } - 4 x - 15$$

Omil

$$\left(x-\left(2-\sqrt{19}\right)\right)\left(x-\left(\sqrt{19}+2\right)\right)$$

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.

$$x^{2}-4x-15=0$$

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.

$$x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\left(-15\right)}}{2}$$

-4 kvadratini chiqarish.

$$x=\frac{-\left(-4\right)±\sqrt{16-4\left(-15\right)}}{2}$$

-4 ni -15 marotabaga ko'paytirish.

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

16 ni 60 ga qo'shish.

$$x=\frac{-\left(-4\right)±\sqrt{76}}{2}$$

76 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-4\right)±2\sqrt{19}}{2}$$

-4 ning teskarisi 4 ga teng.

$$x=\frac{4±2\sqrt{19}}{2}$$

x=\frac{4±2\sqrt{19}}{2} tenglamasini yeching, bunda ± musbat. 4 ni 2\sqrt{19} ga qo'shish.

$$x=\frac{2\sqrt{19}+4}{2}$$

4+2\sqrt{19} ni 2 ga bo'lish.

$$x=\sqrt{19}+2$$

x=\frac{4±2\sqrt{19}}{2} tenglamasini yeching, bunda ± manfiy. 4 dan 2\sqrt{19} ni ayirish.

$$x=\frac{4-2\sqrt{19}}{2}$$

4-2\sqrt{19} ni 2 ga bo'lish.

$$x=2-\sqrt{19}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun 2+\sqrt{19} ga va x_{2} uchun 2-\sqrt{19} ga bo‘ling.

$$x^{2}-4x-15=\left(x-\left(\sqrt{19}+2\right)\right)\left(x-\left(2-\sqrt{19}\right)\right)$$

Baholash

$$x^{2}-4x-15$$