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zay179

20.07.2019 •

Mathematics

Solve the following quadratic equation using the quadratic formula. 5x^2 − 8x + 5 = 0 write the solutions in the following form, where r, s, and t are integers, and the fractions are in simplest form. x = r − si/t,x = r + si/t

Solve the following quadratic equation using the quadratic formula. 5x^2 − 8x + 5 = 0 write the solu

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Ответ:

jessnolonger

13.03.2022

Quadratic equations can be solved using several methods; one of them, is by using quadratic formula

The solution to 5x^2 - 8x + 5 = 0 is: $x = \frac{4 + 3i}{5}, x = \frac{4 - 3i}{5}$

The equation is given as:

5x^2 - 8x + 5 = 0

The quadratic formula is:

$x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

In the given equation;

$a = 5\\b = -8\\c = 5$

So:

$x = \frac{-(-8) \± \sqrt{(-8)^2 - 4 \times 5 \times 5}}{2 \times 5}$

$x = \frac{8 \± \sqrt{-36}}{10}$

Expand

$x = \frac{8 \± \sqrt{36} \times \sqrt{-1}}{10}$

$x = \frac{8 \± 6 \times \sqrt{-1}}{10}$

In complex numbers;

$i = \sqrt{-1}$

So, we have:

$x = \frac{8 \± 6 \times i}{10}$

$x = \frac{8 \± 6i}{10}$

Simplify

$x = \frac{4 \± 3i}{5}$

Split

$x = \frac{4 + 3i}{5}, x = \frac{4 - 3i}{5}$

Hence, the solution to 5x^2 - 8x + 5 = 0 is: $x = \frac{4 + 3i}{5}, x = \frac{4 - 3i}{5}$

Read more about quadratic formulas at:

link

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Ответ:

john67728

13.03.2022

$ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\x_1=\dfrac{-b-\sqrt\Delta}{2a};\ x_2=\dfrac{-b+\sqrt\Delta}{2a}$

$5x^2-8x+5=0\to a=5;\ b=-8;\ c=5\\\\\Delta=(-8)^2-4\cdot5\cdot5=64-100=-36\\\\\sqrt\Delta=\sqrt{-36}=6i$

$x_1=\dfrac{-(-8)-6i}{2\cdot5}=\dfrac{8-6i}{10}=\dfrac{4-3i}{5}\\\\x_2=\dfrac{-(-8)+6i}{2\cdot5}=\dfrac{8+6i}{10}=\dfrac{4+3i}{5}$

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Ответ:

maxgeacryne5573

12.06.2020

Well is there a particular reason why your single are toxic or not loyal.

Step-by-step explanation:

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