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## the function f(x) is defined by f(x)=x^2+3x-10?

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

given x^2 + 13x − 30 = x^2 + kx + 30

∴ 13x − kx = 60

∴ (13 − k)x = 60

∴ 13 − k = 60/x

∴ 13 − 60/x = k

however is you meant f(x + 5) = x^2 + kx − 30 instead

given x^2 + 13x − 30 = x^2 + kx − 30

∴ 13x = kx

∴ k = 13

now f(x + 5) = x^2 + 13x − 30

∴ f(x + 5) = x^2 + 15x − 2x − 30

∴ f(x + 5) = x(x + 15) − 2(x + 15)

∴ f(x + 5) = (x + 15)(x − 2)

∴ when f(x + 5) = 0 then x + 15 = 0 and x − 2 =0

∴ smallist x = -15

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