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If 3 is a zero of the polynomial 2x^(2)+...

If 3 is a zero of the polynomial `2x^(2)+x+k`, find the value of k.

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To find the value of \( k \) in the polynomial \( 2x^2 + x + k \) given that 3 is a zero of the polynomial, we can follow these steps: ### Step-by-step Solution: 1. **Understand the meaning of a zero of a polynomial**: If 3 is a zero of the polynomial \( 2x^2 + x + k \), it means that when we substitute \( x = 3 \) into the polynomial, the result should be zero. 2. **Substitute \( x = 3 \) into the polynomial**: \[ 2(3)^2 + (3) + k = 0 \] 3. **Calculate \( 3^2 \)**: \[ 3^2 = 9 \] 4. **Substitute \( 9 \) back into the equation**: \[ 2(9) + 3 + k = 0 \] 5. **Multiply \( 2 \) by \( 9 \)**: \[ 18 + 3 + k = 0 \] 6. **Combine the constants**: \[ 21 + k = 0 \] 7. **Isolate \( k \)**: \[ k = -21 \] ### Final Answer: The value of \( k \) is \( -21 \). ---
To find the value of \( k \) in the polynomial \( 2x^2 + x + k \) given that 3 is a zero of the polynomial, we can follow these steps: ### Step-by-step Solution: 1. **Understand the meaning of a zero of a polynomial**: If 3 is a zero of the polynomial \( 2x^2 + x + k \), it means that when we substitute \( x = 3 \) into the polynomial, the result should be zero. 2. **Substitute \( x = 3 \) into the polynomial**: \[ ...
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