If the sum of the zeroes of the quadratic polynomial f(t) = kt² + 2t + 3k is equal to their product, find the value of k

Video Explanation

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Solution

Given polynomial:

f(t) = kt² + 2t + 3k

Step 1: Use the Relationship Between Zeros and Coefficients

Let the zeroes of the polynomial be α and β.

For a quadratic polynomial at² + bt + c:

α + β = −b/a
αβ = c/a

Comparing f(t) = kt² + 2t + 3k with at² + bt + c:

a = k,   b = 2,   c = 3k

α + β = −2/k

αβ = 3k/k = 3

Step 2: Use the Given Condition

According to the question:

α + β = αβ

∴ −2/k = 3

Step 3: Find the Value of k

−2 = 3k

∴ k = −2/3

Final Answer

The value of k = −2/3.

Conclusion

Thus, if the sum of the zeroes of the quadratic polynomial f(t) = kt² + 2t + 3k is equal to their product, then the value of k is −2/3.