haverstickw
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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 5x2 8x 5 0 Write the solutions in the following form where r s and t are integers and the fra class=

Respuesta :

gmany
[tex]ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\x_1=\dfrac{-b-\sqrt\Delta}{2a};\ x_2=\dfrac{-b+\sqrt\Delta}{2a}[/tex]

[tex]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[/tex]

[tex]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}[/tex]
MrRoyal

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

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

The equation is given as:

[tex]5x^2 - 8x + 5 = 0[/tex]

The quadratic formula is:

[tex]x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]

In the given equation;

[tex]a = 5\\b = -8\\c = 5[/tex]

So:

[tex]x = \frac{-(-8) \± \sqrt{(-8)^2 - 4 \times 5 \times 5}}{2 \times 5}[/tex]

[tex]x = \frac{8 \± \sqrt{-36}}{10}[/tex]

Expand

[tex]x = \frac{8 \± \sqrt{36} \times \sqrt{-1}}{10}[/tex]

[tex]x = \frac{8 \± 6 \times \sqrt{-1}}{10}[/tex]

In complex numbers;

[tex]i = \sqrt{-1}[/tex]

So, we have:

[tex]x = \frac{8 \± 6 \times i}{10}[/tex]

[tex]x = \frac{8 \± 6i}{10}[/tex]

Simplify

[tex]x = \frac{4 \± 3i}{5}[/tex]

Split

[tex]x = \frac{4 + 3i}{5}, x = \frac{4 - 3i}{5}[/tex]

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

Read more about quadratic formulas at:

https://brainly.com/question/9701183

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