To find the value of [tex]\( k \)[/tex] given that one solution of the quadratic equation [tex]\( x^2 - kx + 21 = 0 \)[/tex] is [tex]\( x = 3 \)[/tex], we can follow these steps:
1. Substitute the known solution into the quadratic equation:
Given that [tex]\( x = 3 \)[/tex] is a solution, substitute [tex]\( x = 3 \)[/tex] into the equation:
[tex]\[
(3)^2 - k(3) + 21 = 0
\][/tex]
2. Simplify the equation:
Calculate [tex]\( 3^2 \)[/tex]:
[tex]\[
9 - 3k + 21 = 0
\][/tex]
3. Combine like terms:
Combine the constant terms on the left-hand side:
[tex]\[
30 - 3k = 0
\][/tex]
4. Solve for [tex]\( k \)[/tex]:
Isolate [tex]\( k \)[/tex] on one side of the equation. To do this, first move [tex]\( -3k \)[/tex] to the right-hand side:
[tex]\[
30 = 3k
\][/tex]
Next, divide both sides by 3 to solve for [tex]\( k \)[/tex]:
[tex]\[
k = \frac{30}{3}
\][/tex]
Therefore,
[tex]\[
k = 10
\][/tex]
So, the value of [tex]\( k \)[/tex] is [tex]\( 10 \)[/tex].
