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Which values of x satisfy this equation? 2x2−3x+4=0

A x=−34+23√4i and x=−34−23√4i B x=34+23√4i and x=34−23√4i C x=−34+41√4 and x=−34−41√4 D x=34+41√4 and x=34−41√4

Respuesta :

frika

Answer:

[tex]x_1=\dfrac{3-i\sqrt{23}}{4}\\ \\x_2=\dfrac{3+i\sqrt{23}}{4}[/tex]

Step-by-step explanation:

Given:

Quadratic equation [tex]2x^2-3x+4=0[/tex]

Find: [tex]x[/tex]

Solution:

1. [tex]a=2,\ b=-3,\ c=4[/tex]

Find the discriminant

[tex]D=b^2-4ac\\ \\=(-3)^2-4\cdot 2\cdot 4\\ \\=9-32\\ \\=-23[/tex]

Note that [tex]i^2=-1,[/tex] then

[tex]D=-23=23i^2[/tex]

Find x:

[tex]x_{1,2}=\dfrac{-b\pm \sqrt{d}}{2a}\\ \\x_1=\dfrac{-(-3)-\sqrt{23i^2}}{2\cdot 2}=\dfrac{3-i\sqrt{23}}{4}\\ \\x_2=\dfrac{-(-3)+\sqrt{23i^2}}{2\cdot 2}=\dfrac{3+i\sqrt{23}}{4}[/tex]

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