Question

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

Answer 1

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:

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