If one of the zero of the quadratic polynomial f(x) = 4x² − 8kx − 9 is the negative of the other, find the value of k

Video Explanation

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Solution

Given polynomial:

f(x) = 4x² − 8kx − 9

Step 1: Use the Given Condition

Let the zeros of the polynomial be α and β.

According to the question:

α = −β

∴ α + β = 0

Step 2: Use the Relationship Between Zeros and Coefficients

For a quadratic polynomial ax² + bx + c:

α + β = −b/a

Comparing f(x) = 4x² − 8kx − 9 with ax² + bx + c:

a = 4,   b = −8k

α + β = −(−8k)/4 = 8k/4 = 2k

Step 3: Find the Value of k

Since α + β = 0,

2k = 0

∴ k = 0

Final Answer

The value of k = 0.

Conclusion

Thus, if one zero of the quadratic polynomial f(x) = 4x² − 8kx − 9 is the negative of the other, then the value of k is 0.