Question

Find all complex solutions

4x^2-5x+2=0

Answer 1

9514 1404 393

Answer:

x = 5/8 ± i(√7)/8

Explanation:

Comparing the given equation to the standard form for the quadratic, ...

ax² +bx +c = 0

we see that we have a=4, b=-5, c=2. This lets us use the quadratic formula to find the solutions:

`x=(-b\pm√(b^2-4ac))/(2a)\\\\x=(-(-5)\pm√((-5)^2-4(4)(2)))/(2(4))=(5\pm√(-7))/(8)\\\\x=\left\{(5)/(8)-(√(7))/(8)i,(5)/(8)+(√(7))/(8)i\right\}`