Quadratic equation problem help please!?

Question

need some help with a quadratic equation containing an imaginary number:

2x^2-ix+3 = 0

A= 2
B= -i
C= 3

The answer should be:

3/2i, and -i

Answer 1

The quadratic equation is 2x² - ix + 3 = 0.

Use quadratic formula to find roots of the related quadratic equation.

Solution, x = [ - b ± √(b² - 4ac) ]/2a.

Compare the given equation with standard form of quadratic equation : ax² + bx + c = 0.

a = 2, b = - i, and c = 3.

Solution, x = [ - (- i) ± √((- i)² - 4(2)(3)) ]/2(2)

= [ i ± √ (i² - 24) ]/4

Substitute i² = - 1.

= [ i ± √ (- 1 - 24) ]/4

= [ i ± √(- 25)]/4

Substitute - 1 = i².

= [ i ± √(i²25)]/4

= [ i ± 5i]/4.

⇒ x = [ i + 5i]/4 and x = [ i - 5i]/4

x = 6i/4 and x = - 4i/4

x = 3i/2 and x = - i.

Solution of the quadratic equation is x = 3i/2 and x = - i.