Final answer:
The zeros of the quadratic function f(x) = 2x² + 8x - 3 are calculated using the quadratic formula, yielding the answers x = -2 + √11 and x = -2 - √11, which corresponds to option (b).
Step-by-step explanation:
The zeros of a quadratic function are the values of x that make the function equal to zero. To find the zeros of the given function f(x) = 2x² + 8x - 3, we can apply the quadratic formula, which is -b ± √(b² - 4ac) / (2a) where a, b, and c are coefficients from the quadratic equation ax² + bx + c = 0.
In this case, a = 2, b = 8, and c = -3. Substitute these values into the quadratic formula to find the zeros:
-8 ± √(8² - 4×2×(-3)) / (2×2)
Computing the discriminant gives us:
√(64 + 24) = √88
So the solutions are:
-8 ± √88 / 4
The square root of 88 can be simplified to √(4×22), which is 2√11. Therefore, the zeros of the quadratic function are x = -2 + √11 and x = -2 - √11, which corresponds to option (b).