h(t)=-5t^2+5t+5 eching

$$h ( t ) = - 5 t ^ { 2 } + 5 t + 5$$

Omil

$$-5\left(t-\frac{1-\sqrt{5}}{2}\right)\left(t-\frac{\sqrt{5}+1}{2}\right)$$

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.

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

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.

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

5 kvadratini chiqarish.

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

-4 ni -5 marotabaga ko'paytirish.

$$t=\frac{-5±\sqrt{25+20\times 5}}{2\left(-5\right)}$$

20 ni 5 marotabaga ko'paytirish.

$$t=\frac{-5±\sqrt{25+100}}{2\left(-5\right)}$$

25 ni 100 ga qo'shish.

$$t=\frac{-5±\sqrt{125}}{2\left(-5\right)}$$

125 ning kvadrat ildizini chiqarish.

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

2 ni -5 marotabaga ko'paytirish.

$$t=\frac{-5±5\sqrt{5}}{-10}$$

t=\frac{-5±5\sqrt{5}}{-10} tenglamasini yeching, bunda ± musbat. -5 ni 5\sqrt{5} ga qo'shish.

$$t=\frac{5\sqrt{5}-5}{-10}$$

-5+5\sqrt{5} ni -10 ga bo'lish.

$$t=\frac{1-\sqrt{5}}{2}$$

t=\frac{-5±5\sqrt{5}}{-10} tenglamasini yeching, bunda ± manfiy. -5 dan 5\sqrt{5} ni ayirish.

$$t=\frac{-5\sqrt{5}-5}{-10}$$

-5-5\sqrt{5} ni -10 ga bo'lish.

$$t=\frac{\sqrt{5}+1}{2}$$

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{5}}{2} ga va x_{2} uchun \frac{1+\sqrt{5}}{2} ga bo‘ling.

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

Baholash

$$5\left(1+t-t^{2}\right)$$