Solve the quadratic equation 2x2+5x−3=0 using the quadratic formula.(2 points) x = ,
The quadratic equation is in the form ax^2 + bx + c = 0. In this case, a = 2, b = 5, and c = -3.
The quadratic formula is:
x = [-b ± sqrt(b^2 - 4ac)] / 2a
Plugging in the values, we get:
x = [-5 ± sqrt(5^2 - 4*2*(-3))] / 2*2
x = [-5 ± sqrt(25 + 24)] / 4
x = [-5 ± sqrt(49)] / 4
x = [-5 ± 7] / 4
This gives two possible solutions:
x1 = (-5 + 7) / 4 = 2 / 4 = 0.5
x2 = (-5 - 7) / 4 = -12 / 4 = -3
Therefore, the solutions to the quadratic equation 2x^2 + 5x - 3 = 0 are x = 0.5 and x = -3.