First, let's find the value of k by expanding f(x + 5):
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 f(x + 5) with x² + kx + 30, we see that k = 13.
Next, let's find the smallest zero of f(x + 5) by setting f(x + 5) = 0 and solving for x:
x² + 13x + 30 = 0
(x + 3)(x + 10) = 0
This gives us two solutions: x = -3 and x = -10. Since we are looking for the smallest zero of f(x + 5), we want to use the solution x = -10.
Therefore, the smallest zero of f(x + 5) is 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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