Give exact and approximate solutions to three decimal places.
X^2-5x+3=0
Use the formula
exact values:
x = (5 ± √13)/2
Use your calculator to find appr. values
To find the exact and approximate solutions of the quadratic equation x^2 - 5x + 3 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Here, a = 1, b = -5, and c = 3. Plugging in the values, we get:
x = (5 ± √((-5)^2 - 4(1)(3))) / (2(1))
Simplifying further:
x = (5 ± √(25 - 12)) / 2
x = (5 ± √13) / 2
So, the exact solutions of the equation x^2 - 5x + 3 = 0 are:
x = (5 + √13) / 2 and x = (5 - √13) / 2
To find the approximate solutions to three decimal places, we can evaluate these expressions using a calculator:
x ≈ 3.302 and x ≈ 1.698
Therefore, the exact solutions are (5 + √13) / 2 and (5 - √13) / 2, and the approximate solutions to three decimal places are 3.302 and 1.698.