Find the zeros of the following expressions:
1) 2t² - 50
2) 3u² - 12

To find the zeros of the given expressions, set each expression to zero and solve for the variable. The zeros for 2 t 2 − 50 are t = 5 and t = − 5 , while the zeros for 3 u 2 − 12 are u = 2 and u = − 2 . This method involves isolating the variable and taking square roots, considering both positive and negative solutions.
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Answered by Anonymous | 2025-07-04

To find the zeros of the quadratic expressions, we need to set each expression equal to zero and solve for the variable.

Expression: 2 t 2 − 50
First, set the equation to zero:


2 t 2 − 50 = 0
Next, solve for [tex]t[/tex] by isolating [tex]t^2[/tex]:

2 t 2 = 50
Divide both sides by 2:

t 2 = 25
Take the square root of both sides to solve for [tex]t[/tex]:

t = ± 5
Therefore, the zeros of [tex]2t^2 - 50[/tex] are [tex]t = 5[/tex] and [tex]t = -5[/tex].


Expression: 3 u 2 − 12
First, set the equation to zero:


3 u 2 − 12 = 0
Solve for [tex]u[/tex] by isolating [tex]u^2[/tex]:

3 u 2 = 12
Divide both sides by 3:

u 2 = 4
Take the square root of both sides to solve for [tex]u[/tex]:

u = ± 2
Therefore, the zeros of [tex]3u^2 - 12[/tex] are [tex]u = 2[/tex] and [tex]u = -2[/tex].

In summary, we found the zeros for each quadratic expression by isolating the squared term and taking the square root of each side, which effectively gives us the values of the variable ( t or u ) that make the expression equal to zero.

Answered by LiamAlexanderSmith | 2025-07-06