To find the value of k, we need to expand f(x+5) using the given definition of f(x):
f(x+5) = (x+5)² + 3(x+5) - 10
f(x+5) = x² + 10x + 25 + 3x + 15 - 10
f(x+5) = x² + 13x + 30
Comparing this result with x² + kx + 30, we see that k = 13.
To find the smallest zero of f(x + 5), we need to solve for x when f(x+5) = 0:
0 = x² + 13x + 30
0 = (x + 3)(x + 10)
The zeros are x = -3 and x = -10. Since we need the smallest zero, x = -10.
The function f is defined by f(x) = x²+3x-10.
If f (x + 5) = x² + kx + 30, k= ____ Find the smallest zero of f(x + 5). x = ______
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