If one of the zeroes of the quadratic polynomial (k − 1)x² + kx + 1 is −3, find the value of k

Video Explanation

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Given

Polynomial: f(x) = (k − 1)x² + kx + 1

One zero of the polynomial = −3

To Find

The value of k.

Solution

Since −3 is a zero of the polynomial, by the Factor Theorem:

f(−3) = 0

Step 1: Substitute x = −3

f(−3) = (k − 1)(−3)² + k(−3) + 1

= 9(k − 1) − 3k + 1

= 9k − 9 − 3k + 1

= 6k − 8

Step 2: Solve for k

6k − 8 = 0

6k = 8

k = 4/3

Final Answer

k = 4/3

Conclusion

Hence, if one of the zeroes of the quadratic polynomial (k − 1)x² + kx + 1 is −3, then the value of k is 4/3.