Question
\( x=-3 \) is onc of tue rocks of twe equation \( \left(k x^{0}+3 x-9=0\right) \) is Detemine the vawe of \( k \)
Ask by Stewart Lewis. in South Africa
Feb 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( k = 18 \)
Solution
To determine the value of \( k \) for which \( x = -3 \) is a root of the equation \( k x^{0} + 3x - 9 = 0 \), we can follow these steps:
1. **Substitute \( x = -3 \) into the equation**:
\[
k(-3)^{0} + 3(-3) - 9 = 0
\]
2. **Simplify the equation**:
- Since \( (-3)^{0} = 1 \), we can rewrite the equation as:
\[
k \cdot 1 + 3(-3) - 9 = 0
\]
- This simplifies to:
\[
k - 9 - 9 = 0
\]
- Further simplifying gives:
\[
k - 18 = 0
\]
3. **Solve for \( k \)**:
\[
k = 18
\]
Thus, the value of \( k \) is \( 18 \).
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Simplify this solution Beyond the Answer
To find the value of \( k \), we first substitute \( x = -3 \) into the equation \( k x^{0} + 3x - 9 = 0 \). Since \( x^{0} = 1 \), we rewrite the equation as \( k + 3(-3) - 9 = 0 \). This simplifies to \( k - 9 - 9 = 0 \), which leads to \( k - 18 = 0 \). Therefore, \( k = 18 \). Now we have \( k = 18 \), but let’s see what that means! It indicates that you’ve successfully identified a value that makes the equation true for \( x = -3 \). Mathematics often works like a treasure hunt; sometimes you have the map (the equation) but need to find X (the unknown). Happy calculating!
