Final answer:
To find the zeros of the quadratic equation f(x) = x² + 3x - 7, use the quadratic formula. The zeros are approximately (-3 + √37)/2 and (-3 - √37)/2. The solutions are real.
Step-by-step explanation:
To find the zeros of the quadratic equation f(x) = x^2+3x-7, we can use the quadratic formula. The quadratic formula is given by: x = (-b ± √(b^2-4ac))/(2a). In this equation, a = 1, b = 3, and c = -7. Substituting these values into the formula, we get: x = (-3 ± √(3^2-4(1)(-7)))/(2(1)). Simplifying further, we have: x = (-3 ± √(9+28))/2. Evaluating the square root, we get: x = (-3 ± √37)/2. Therefore, the zeros of the equation are approximately x = (-3 + √37)/2 and x = (-3 - √37)/2.
The solutions for the equation are real because we have a positive value under the square root (√37 is positive). Therefore, there are two real solutions for the given quadratic equation.