Question

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

Answer 1

`x_1=(3-i√(23))/(4)\\ \\x_2=(3+i√(23))/(4)`

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)=(-b\pm √(d))/(2a)\\ \\x_1=(-(-3)-√(23i^2))/(2\cdot 2)=(3-i√(23))/(4)\\ \\x_2=(-(-3)+√(23i^2))/(2\cdot 2)=(3+i√(23))/(4)`