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If [tex]\( x = 2 \)[/tex] is a solution of [tex]\( x^2 - 3x + k \)[/tex], find the value of [tex]\( k \)[/tex].

Sagot :

GinnyAnswer
To find the value of [tex]\( k \)[/tex] in the equation [tex]\( x^2 - 3x + k = 2 \)[/tex], let's follow these steps:

1. Start with the given equation:
[tex]\[ x^2 - 3x + k = 2 \][/tex]

2. Rearrange the equation to isolate [tex]\( k \)[/tex]:
[tex]\[ x^2 - 3x + k - 2 = 0 \][/tex]
This can be rewritten as:
[tex]\[ x^2 - 3x + (k - 2) = 0 \][/tex]

3. Solve for [tex]\( k \)[/tex]:
Now, let's assume a particular value of [tex]\( x \)[/tex] to find [tex]\( k \)[/tex].

Given [tex]\( x = 2 \)[/tex]:

Plug [tex]\( x = 2 \)[/tex] into the equation:
[tex]\[ (2)^2 - 3(2) + (k - 2) = 0 \][/tex]
Simplify this equation step-by-step:
[tex]\[ 4 - 6 + k - 2 = 0 \][/tex]
Combine like terms:
[tex]\[ 4 - 6 - 2 + k = 0 \][/tex]
Simplify further:
[tex]\[ -4 + k = 0 \][/tex]

4. Isolate [tex]\( k \)[/tex]:
Add 4 to both sides of the equation to solve for [tex]\( k \)[/tex]:
[tex]\[ k = 4 \][/tex]

So, the value of [tex]\( k \)[/tex] is:
[tex]\[ k = 4 \][/tex]
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