To find k, we need to set f(x+5) equal to x² + kx + 30:
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
Now compare this to x² + kx + 30:
k = 13
To find the smallest zero of f(x + 5), we need to set f(x + 5) equal to zero and solve for x:
f(x + 5) = 0
x² + 13x + 30 = 0
(x + 3)(x + 10) = 0
This equation gives us two possible solutions: x = -3 or x = -10. The smallest zero is -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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