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vladimir2022 [97]
3 years ago
10

Find the smallest zero of f(x+5)

Mathematics
2 answers:
podryga [215]3 years ago
7 0

ANSWER

1. k=13

2. x=-10

EXPLANATION

The given function is

f(x) =  {x}^{2}   + 3x  - 10

To find f(x+5), plug in (x+5) wherever you see x.

This implies that:

f(x) =  {(x + 5)}^{2}   + 3(x + 5) - 10

Expand:

f(x) =   {x}^{2}    + 10x + 25+ 3x + 15- 10

Simplify to obtain

f(x) =   {x}^{2}    + 13x + 30

We now compare with,

f(x) =   {x}^{2}    + kx + 30

This implies that:

k = 13

To find the smallest zero of f(x+5), we equate the function to zero and solve for x.

{x}^{2}    + 13x + 30 = 0

{x}^{2}   + 10x + 3x + 30 = 0

x(x + 10) + 3(x + 10) = 0

(x + 3)(x + 10) = 0

x =  - 10 \: or \: x =  - 3

The smallest zero is -10.

Mariulka [41]3 years ago
4 0

Answer:

k=13 while x =-10 :)

Step-by-step explanation:

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