Question

What are the solutions to the quadratic equation x^2-3x+4=0

Answer 1

`x=(3)/(2) - i(√(7))/(2)`

`x=(3)/(2) + i(√(7))/(2)`

Explanation:

We can use the quadratic formula to solve the equation:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = -3, and c = 4. Substituting these values into the formula, we get:

x = (3 ± sqrt((-3)^2 - 4(1)(4))) / 2(1)

x = (3 ± sqrt(9 - 16)) / 2

x = (3 ± sqrt(-7)) / 2

Since the square root of a negative number is not a real number, the solutions to the quadratic equation are complex numbers. Therefore, the answer is:

`x=(3)/(2)+i(√(7) )/(2)`

`x=(3)/(2) - i(√(7))/(2)`