f(x)=1+x^2+7x eching

$$f ( x ) = 1 + x ^ { 2 } + 7 x$$

Omil

$$\left(x-\frac{-3\sqrt{5}-7}{2}\right)\left(x-\frac{3\sqrt{5}-7}{2}\right)$$

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.

$$x^{2}+7x+1=0$$

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.

$$x=\frac{-7±\sqrt{7^{2}-4}}{2}$$

7 kvadratini chiqarish.

$$x=\frac{-7±\sqrt{49-4}}{2}$$

49 ni -4 ga qo'shish.

$$x=\frac{-7±\sqrt{45}}{2}$$

45 ning kvadrat ildizini chiqarish.

$$x=\frac{-7±3\sqrt{5}}{2}$$

x=\frac{-7±3\sqrt{5}}{2} tenglamasini yeching, bunda ± musbat. -7 ni 3\sqrt{5} ga qo'shish.

$$x=\frac{3\sqrt{5}-7}{2}$$

x=\frac{-7±3\sqrt{5}}{2} tenglamasini yeching, bunda ± manfiy. -7 dan 3\sqrt{5} ni ayirish.

$$x=\frac{-3\sqrt{5}-7}{2}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{-7+3\sqrt{5}}{2} ga va x_{2} uchun \frac{-7-3\sqrt{5}}{2} ga bo‘ling.

$$x^{2}+7x+1=\left(x-\frac{3\sqrt{5}-7}{2}\right)\left(x-\frac{-3\sqrt{5}-7}{2}\right)$$

Baholash

$$x^{2}+7x+1$$