If one zero of the quadratic polynomial x² + 3x + k is 2, find the value of k

Video Explanation

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Given

Quadratic polynomial: f(x) = x² + 3x + k

One zero of the polynomial = 2

To Find

The value of k.

Solution

Since 2 is a zero of the polynomial, by the Factor Theorem:

f(2) = 0

Step 1: Substitute x = 2

f(2) = (2)² + 3(2) + k

= 4 + 6 + k

= 10 + k

Step 2: Solve for k

10 + k = 0

k = −10

Final Answer

The value of k is:

−10

Correct Option

(b) −10

Conclusion

Hence, if one zero of the quadratic polynomial x² + 3x + k is 2, then the value of k is −10.