p(x)=-5x^2-10x-2 eching

$$p ( x ) = - 5 x ^ { 2 } - 10 x - 2$$

Omil

$$-5\left(x-\left(-\frac{\sqrt{15}}{5}-1\right)\right)\left(x-\left(\frac{\sqrt{15}}{5}-1\right)\right)$$

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.

$$-5x^{2}-10x-2=0$$

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.

$$x=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}-4\left(-5\right)\left(-2\right)}}{2\left(-5\right)}$$

-10 kvadratini chiqarish.

$$x=\frac{-\left(-10\right)±\sqrt{100-4\left(-5\right)\left(-2\right)}}{2\left(-5\right)}$$

-4 ni -5 marotabaga ko'paytirish.

$$x=\frac{-\left(-10\right)±\sqrt{100+20\left(-2\right)}}{2\left(-5\right)}$$

20 ni -2 marotabaga ko'paytirish.

$$x=\frac{-\left(-10\right)±\sqrt{100-40}}{2\left(-5\right)}$$

100 ni -40 ga qo'shish.

$$x=\frac{-\left(-10\right)±\sqrt{60}}{2\left(-5\right)}$$

60 ning kvadrat ildizini chiqarish.

$$x=\frac{-\left(-10\right)±2\sqrt{15}}{2\left(-5\right)}$$

-10 ning teskarisi 10 ga teng.

$$x=\frac{10±2\sqrt{15}}{2\left(-5\right)}$$

2 ni -5 marotabaga ko'paytirish.

$$x=\frac{10±2\sqrt{15}}{-10}$$

x=\frac{10±2\sqrt{15}}{-10} tenglamasini yeching, bunda ± musbat. 10 ni 2\sqrt{15} ga qo'shish.

$$x=\frac{2\sqrt{15}+10}{-10}$$

10+2\sqrt{15} ni -10 ga bo'lish.

$$x=-\frac{\sqrt{15}}{5}-1$$

x=\frac{10±2\sqrt{15}}{-10} tenglamasini yeching, bunda ± manfiy. 10 dan 2\sqrt{15} ni ayirish.

$$x=\frac{10-2\sqrt{15}}{-10}$$

10-2\sqrt{15} ni -10 ga bo'lish.

$$x=\frac{\sqrt{15}}{5}-1$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun -1-\frac{\sqrt{15}}{5} ga va x_{2} uchun -1+\frac{\sqrt{15}}{5} ga bo‘ling.

$$-5x^{2}-10x-2=-5\left(x-\left(-\frac{\sqrt{15}}{5}-1\right)\right)\left(x-\left(\frac{\sqrt{15}}{5}-1\right)\right)$$

Baholash

$$-5x^{2}-10x-2$$