f(x)=-2x^2+5x+6 eching

$$f ( x ) = - 2 x ^ { 2 } + 5 x + 6$$

Omil

$$-2\left(x-\frac{5-\sqrt{73}}{4}\right)\left(x-\frac{\sqrt{73}+5}{4}\right)$$

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.

$$-2x^{2}+5x+6=0$$

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.

$$x=\frac{-5±\sqrt{5^{2}-4\left(-2\right)\times 6}}{2\left(-2\right)}$$

5 kvadratini chiqarish.

$$x=\frac{-5±\sqrt{25-4\left(-2\right)\times 6}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{25+8\times 6}}{2\left(-2\right)}$$

8 ni 6 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{25+48}}{2\left(-2\right)}$$

25 ni 48 ga qo'shish.

$$x=\frac{-5±\sqrt{73}}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-5±\sqrt{73}}{-4}$$

x=\frac{-5±\sqrt{73}}{-4} tenglamasini yeching, bunda ± musbat. -5 ni \sqrt{73} ga qo'shish.

$$x=\frac{\sqrt{73}-5}{-4}$$

-5+\sqrt{73} ni -4 ga bo'lish.

$$x=\frac{5-\sqrt{73}}{4}$$

x=\frac{-5±\sqrt{73}}{-4} tenglamasini yeching, bunda ± manfiy. -5 dan \sqrt{73} ni ayirish.

$$x=\frac{-\sqrt{73}-5}{-4}$$

-5-\sqrt{73} ni -4 ga bo'lish.

$$x=\frac{\sqrt{73}+5}{4}$$

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right) formulasi yordamida amalni hisoblang. x_{1} uchun \frac{5-\sqrt{73}}{4} ga va x_{2} uchun \frac{5+\sqrt{73}}{4} ga bo‘ling.

$$-2x^{2}+5x+6=-2\left(x-\frac{5-\sqrt{73}}{4}\right)\left(x-\frac{\sqrt{73}+5}{4}\right)$$

Baholash

$$6+5x-2x^{2}$$