Solve the quadratic equation x2+16=0
. Express its solutions in the form a±bi
.(1 point)
To solve the quadratic equation x^2 + 16 = 0, we can use the quadratic formula. The quadratic formula is given as:
x = (-b ± √(b^2 - 4ac)) / (2a)
For this equation, a = 1, b = 0, and c = 16. Plugging these values into the quadratic formula, we get:
x = (-0 ± √(0^2 - 4(1)(16))) / (2(1))
x = (± √(-64)) / 2
Since we have a square root of a negative number, we can simplify this further using the imaginary unit, i. We know that √(-1) = i. Therefore, we can rewrite √(-64) as 8i:
x = (± 8i) / 2
x = ± 4i
Therefore, the solutions to the quadratic equation x^2 + 16 = 0 are x = 4i and x = -4i.