Use the quadratic formula to solve the quadratic equation 2x^2−9x+11=0 . Express its solutions in the form a±bi . (1 point)
The quadratic formula states that for a quadratic equation of the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac))/2a
For the given equation 2x^2 - 9x + 11 = 0, we have:
a = 2, b = -9, c = 11
Applying the quadratic formula:
x = (-(-9) ± √((-9)^2 - 4(2)(11)))/ (2(2))
x = (9 ± √(81 - 88))/4
x = (9 ± √(-7))/4
Since the discriminant (√(-7)) is negative, the solutions of the quadratic equation are in the form of a±bi. Thus, the solutions are:
x = (9 ± √7i)/4