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If one zero of the polynomial [tex][tex]$x^2 + 3x + k$[/tex][/tex] is 2, then find the value of [tex][tex]$k$[/tex][/tex].

Sagot :

To find the value of [tex]\( k \)[/tex] such that one zero of the polynomial [tex]\( x^2 + 3x + k \)[/tex] is 2, follow these steps:

1. Recall the general form of a polynomial and how zeros of the polynomial work. If [tex]\( r \)[/tex] is a zero of the polynomial [tex]\( f(x) \)[/tex], then [tex]\( f(r) = 0 \)[/tex].

2. Given [tex]\( f(x) = x^2 + 3x + k \)[/tex] and knowing that one zero of this polynomial is 2, substitute [tex]\( x = 2 \)[/tex] into the polynomial and set it equal to zero.

[tex]\[ f(2) = (2)^2 + 3(2) + k = 0 \][/tex]

3. Simplify the equation:

[tex]\[ 4 + 6 + k = 0 \][/tex]

4. Combine like terms:

[tex]\[ 10 + k = 0 \][/tex]

5. Solve for [tex]\( k \)[/tex] by isolating it on one side of the equation:

[tex]\[ k = -10 \][/tex]

Thus, the value of [tex]\( k \)[/tex] is [tex]\( -10 \)[/tex].