To find k, we need to expand f(x+5) using the given function f(x) = x^2 + 3x - 10.
f(x+5) = (x+5)^2 + 3(x+5) - 10
f(x+5) = x^2 + 10x + 25 + 3x + 15 - 10
f(x+5) = x^2 + 13x + 30
Comparing this to x^2 + kx + 30, we can see that k = 13.
To find the smallest zero of f(x+5), we set f(x+5) equal to zero and solve for x:
x^2 + 13x + 30 = 0
This is a quadratic equation that can be factored as:
(x + 3)(x + 10) = 0
Setting each factor to zero gives us the solutions x = -3 or x = -10. The smallest zero is x = -10.
The function f is defined by f(x)=x^2+3x-10
If f(x+5)=x^2+kx+30, k=____ Find the smallest zero of f(x+5). x=____
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