Respuesta :
Answer:
x=2+i, x=2-i
Step-by-step explanation:
x^2-4x+5=0
Apply the quadratic formula.
There are are no real solutions for this equation.
What is a quadratic equation?
An equation whose highest degree is 2, is called a quadratic equation.
How to solve a quadratic equation?
We can solve a quadratic equation by two ways:
- Factorization- If the quadratic expression is factorizable then we can factorize it and equate it to 0. Then we can apply the concept that when product of two or more expressions is 0 then at least one of the expression or both must be 0
- By Shreedhar Acharya formula- A quadratic equation of the [tex]ax^{2} +bx+c=0[/tex] form can be solved by the formula given below:
[tex]x=\frac{-b-\sqrt{b^{2}-4ac } }{2a}[/tex]
or
[tex]x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]
- This [tex]\sqrt{b^{2}-4ac }[/tex] is called discriminant.
- If the discriminant is negative, then the equation have no real solution.
How to find the solutions of x²-4x+5=0?
Comparing with the standard equation [tex]ax^{2} +bx+c=0[/tex],
- a = 1
- b = -4
- c = 5
How to check the discriminant?
∴ Discriminant = [tex]\sqrt{b^{2}-4ac }[/tex] = [tex]\sqrt{-4}[/tex]
- Here, the discriminant is negative, so there are no real solutions.
- There are imaginary solutions.
Find out more about 'Quadratic Equation' here: brainly.com/question/1214333
#SPJ2
