To find the x-intercepts of the quadratic function f(x) = 3x² + 11x − 42, we can use the quadratic formula:
x=2a−b±b2−4ac
where a = 3, b = 11, and c = -42. Substituting these values into the formula, we get:
x=2(3)−11±112−4(3)(−42)
Simplifying the expression under the square root, we get:
x=6−11±205
Therefore, the x-intercepts of the quadratic function f(x) = 3x² + 11x − 42 are approximately:
x1≈−4.08andx2≈3.45