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

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

Omil

$$-2\left(x-\frac{1-\sqrt{41}}{4}\right)\left(x-\frac{\sqrt{41}+1}{4}\right)$$

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.

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

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.

$$x=\frac{-1±\sqrt{1^{2}-4\left(-2\right)\times 5}}{2\left(-2\right)}$$

1 kvadratini chiqarish.

$$x=\frac{-1±\sqrt{1-4\left(-2\right)\times 5}}{2\left(-2\right)}$$

-4 ni -2 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1+8\times 5}}{2\left(-2\right)}$$

8 ni 5 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{1+40}}{2\left(-2\right)}$$

1 ni 40 ga qo'shish.

$$x=\frac{-1±\sqrt{41}}{2\left(-2\right)}$$

2 ni -2 marotabaga ko'paytirish.

$$x=\frac{-1±\sqrt{41}}{-4}$$

x=\frac{-1±\sqrt{41}}{-4} tenglamasini yeching, bunda ± musbat. -1 ni \sqrt{41} ga qo'shish.

$$x=\frac{\sqrt{41}-1}{-4}$$

-1+\sqrt{41} ni -4 ga bo'lish.

$$x=\frac{1-\sqrt{41}}{4}$$

x=\frac{-1±\sqrt{41}}{-4} tenglamasini yeching, bunda ± manfiy. -1 dan \sqrt{41} ni ayirish.

$$x=\frac{-\sqrt{41}-1}{-4}$$

-1-\sqrt{41} ni -4 ga bo'lish.

$$x=\frac{\sqrt{41}+1}{4}$$

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{41}}{4} ga va x_{2} uchun \frac{1+\sqrt{41}}{4} ga bo‘ling.

$$-2x^{2}+x+5=-2\left(x-\frac{1-\sqrt{41}}{4}\right)\left(x-\frac{\sqrt{41}+1}{4}\right)$$

Baholash

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