Find the Zeroes of Quadratic Polynomial and Verify the Relationship Between the Zeroes and it’s Coefficient: T^2-15
By BYJU'S Exam Prep
Updated on: October 17th, 2023
Find the zeros of quadratic polynomial and verify the relationship between the zeros and it’s coefficient: t2-15
We can find out the zeros of the give quadratic equation either by using quadratic formula or directly equating it to 0.
Once we get the zeros, we can verify the result by replacinng t with the zeros respectively and check if the equation is still giving the same result as before or comes equal to 0. Check out the detailed solution below.
Table of content
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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