Solve using qaudractic formula.Then use a calculator to approximate to three decimal places, the solution as rational numbers. X^2-4x+1=0
Quadratic Formula: -b (± square root b^2 - 4ac)divided by 2a
Sub in the numbers.
a = 1
b = 4
c = 1
To solve the quadratic equation x^2 - 4x + 1 = 0 using the quadratic formula, we can follow these steps:
Step 1: Identify the coefficients a, b, and c in the equation.
In our equation, the coefficient a is 1, the coefficient b is -4, and the coefficient c is 1.
Step 2: Plug these values into the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / (2a).
Step 3: Substitute the respective values, we have x = (-( -4) ± √((-4)^2 - 4(1)(1))) / (2(1)).
Step 4: Simplify the equation:
x = (4 ± √(16 - 4)) / 2,
x = (4 ± √12) / 2.
Step 5: Simplify further:
x = (4 ± √(4 · 3)) / 2,
x = (4 ± 2√3) / 2.
Step 6: Divide each term by 2:
x = (2 ± √3).
Now, to approximate the solution as rational numbers using a calculator, we can substitute the values of √3 into the equation.
Approximating the value of √3 to three decimal places, we find that √3 is approximately 1.732.
So, substituting this value, we get:
x ≈ (2 + 1.732) and x ≈ (2 - 1.732).
Evaluating further:
x ≈ 3.732 and x ≈ 0.268.
Therefore, the approximate solutions of the given quadratic equation as rational numbers to three decimal places are x = 3.732 and x = 0.268.