x^2 - 3x + 5 = 0. solve using quadratic formula. show solution
To solve the quadratic equation x^2 - 3x + 5 = 0 using the quadratic formula, we can follow these steps:
Step 1: Identify the coefficients of the quadratic equation:
- The coefficient of x^2 is 1.
- The coefficient of x is -3.
- The constant term is 5.
Step 2: Use the quadratic formula:
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
Plugging in the values for our equation, we get:
x = (-(-3) ± √((-3)^2 - 4(1)(5))) / (2(1))
Step 3: Simplify the quadratic formula:
x = (3 ± √(9 - 20)) / 2
x = (3 ± √(-11)) / 2
Step 4: Determine the nature of the solutions:
Since we have a negative value inside the square root (√(-11)), we can see that the quadratic equation has no real solutions. The solutions are complex.
Therefore, the quadratic equation x^2 - 3x + 5 = 0 has no real solutions.
To solve the quadratic equation x^2 - 3x + 5 = 0 using the quadratic formula, we will apply the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a, b, and c represent the coefficients of x^2, x, and the constant term, respectively.
For the equation x^2 - 3x + 5 = 0, we have:
a = 1, b = -3, and c = 5.
Substituting these values into the quadratic formula, we get:
x = (-(-3) ± √((-3)^2 - 4*1*5)) / (2*1)
Simplifying further:
x = (3 ± √(9 - 20)) / 2
x = (3 ± √(-11)) / 2
Since the discriminant (√(b^2 - 4ac)) under the square root is negative (-11), the equation does not have any real solutions. In this case, we say that the equation has no real roots.
Therefore, the solution to the equation x^2 - 3x + 5 = 0 using the quadratic formula is imaginary, and there are no real values of x that satisfy the equation.
x ^ 2 - 3 x + 5 < 0
In google type:
quadratic equation online
When you see list of results click on:
Free Online Quadratic Equation Solver:Solve by Quadratic Formula
When page be open in rectangle type:
x ^ 2 - 3 x + 5 = 0
and click option: solve it!
You will see solution step-by step