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AnnyKZ [126]
4 years ago
6

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

Mathematics
1 answer:
djyliett [7]4 years ago
6 0

Answer:

x_1=\dfrac{3-i\sqrt{23}}{4}\\ \\x_2=\dfrac{3+i\sqrt{23}}{4}

Step-by-step explanation:

Given:

Quadratic equation 2x^2-3x+4=0

Find: x

Solution:

1. a=2,\ b=-3,\ c=4

Find the discriminant

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

Note that i^2=-1, then

D=-23=23i^2

Find x:

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}

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