Find the Zeroes of Quadratic Polynomial and Verify the Relationship Between the Zeroes and it's Coefficient: T^2-15

Find the Zeros of Quadratic Polynomial and Verify the Relationship Between the Zeros and it's Coefficient: T²-15

Solution:

Using the quadratic formula, we have:

t = (-b ± √(b² - 4ac)) / (2a)

For the equation t² - 15 = 0, where a = 1, b = 0, and c = -15, we substitute the values into the formula:

t = (0 ± √(0² - 4(1)(-15))) / (2(1)) = (± √(0 + 60)) / 2 = (± √60) / 2 = ± √15

Therefore, the solutions to the equation t² - 15 = 0 are t = √15 and t = -√15.

Let's verify the solutions t = ± √15.

For t = √15: (√15)² - 15 = 0 15 - 15 = 0 0 = 0

The equation holds true for t = √15.

For t = -√15: (-√15)² - 15 = 0 15 - 15 = 0 0 = 0

The equation also holds true for t = -√15.

Therefore, both solutions t = ± √15 satisfy the equation t² - 15 = 0.

Answer:

The Solutions to the Equation t² - 15 = 0 are t = √15 and t = -√15

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