Find the exact real solutions, if any, of this quadratic equation. Use any method. If there is no real solution enter NONE in each box.
2x^2-5x+3=0
Is the smaller value none andthe larger value none.
Use the quadratic formula
x = [-b +/- sqrt(b^2-4ac)]/2a
if you do not see how to factor it.
Note that b^2-4ac = 1, so there are real solutions.
This is not a calculus question. it is algebra.
To find the solutions of a quadratic equation, such as 2x^2 - 5x + 3 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, the values of a, b, and c are as follows:
a = 2
b = -5
c = 3
Now let's substitute these values into the quadratic formula and calculate the solutions:
x = (-(-5) ± √((-5)^2 - 4 * 2 * 3)) / (2 * 2)
x = (5 ± √(25 - 24)) / 4
x = (5 ± √1) / 4
Simplifying further:
x = (5 ± 1) / 4
This yields two potential solutions:
x1 = (5 + 1) / 4 = 6 / 4 = 1.5
x2 = (5 - 1) / 4 = 4 / 4 = 1
Therefore, the solutions to the quadratic equation 2x^2 - 5x + 3 = 0 are x = 1.5 and x = 1.