Question 3 of 25Use the quadratic formula to find the solutions to the quadratic equation below.2x2 - 5x + 5 = 0A.B.C.D.
Question
Question 3 of 25
Use the quadratic formula to find the solutions to the quadratic equation below.
Equation:
2x² - 5x + 5 = 0
A.
B.
C.
D.
Solution
The quadratic formula is given by:
x = [-b ± sqrt(b² - 4ac)] / 2a
In the given equation 2x² - 5x + 5 = 0, the coefficients are:
a = 2 b = -5 c = 5
Substitute these values into the quadratic formula:
x = [5 ± sqrt((-5)² - 425)] / 2*2 x = [5 ± sqrt(25 - 40)] / 4 x = [5 ± sqrt(-15)] / 4
Since the value under the square root is negative, the solutions will be complex numbers. We can write sqrt(-15) as i*sqrt(15), where i is the imaginary unit. So the solutions are:
x = [5 ± i*sqrt(15)] / 4
So the solutions to the equation 2x² - 5x + 5 = 0 are x = 5/4 + (sqrt(15)/4)i and x = 5/4 - (sqrt(15)/4)i.
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