Find the Zeros of h(t) = t² − 15 and Verify the Relationship Between Zeros and Coefficients

Video Explanation

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Solution

Given polynomial:

h(t) = t² − 15

Step 1: Find the Zeros of the Polynomial

t² − 15 = 0

t² = 15

t = √15   or   t = −√15

Zeros of the polynomial are √15 and −√15.

Step 2: Identify Coefficients

Comparing h(t) = t² − 15 with at² + bt + c:

a = 1,   b = 0,   c = −15

Step 3: Verify the Relationship

Let α = √15 and β = −√15

Sum of zeros:

α + β = √15 + (−√15) = 0

−b/a = −0/1 = 0

✔ Sum of zeros = −b/a

Product of zeros:

αβ = (√15)(−√15) = −15

c/a = −15/1 = −15

✔ Product of zeros = c/a

Final Answer

Zeros of the polynomial are √15 and −√15.

The relationship between zeros and coefficients is verified.

Conclusion

Thus, for the quadratic polynomial h(t) = t² − 15, the sum and product of zeros satisfy the standard relationships with its coefficients.