Question
What are the zeros of the quadratic function
?
and
and
and
and
Ask by Pope Hardy. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The zeros of the quadratic function
are
and
.
Solution
We start with the quadratic function
To find the zeros, we set
:
The quadratic formula states that, for an equation
the solutions are
Here,
,
, and
. Substitute these values into the quadratic formula:
Simplify the expression:
- Compute
: - Compute the discriminant:
- So, the formula becomes:
Now, simplify the square root. Notice that:
Thus, the expression for
is:
Therefore, the zeros of the quadratic function are:
Comparing this result with the given options, the correct choice is:
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Beyond the Answer
To find the zeros of the quadratic function
, you can use the quadratic formula
. Here,
,
, and
. Plugging in the values gives you
. Thus, the zeros are
!
Looking at the options, the correct zeros are
and
.
Ever wondered how quadratic equations come into play in the real world? They’re all around us! From projectile motion in sports to calculating the optimal price for goods in business, quadratics help model scenarios where things grow or shrink in a parabolic shape. Understanding their zeros can predict key outcomes, making it essential for fields like engineering, finance, and even rocket science!
When solving quadratics, people often forget to carefully compute the discriminant
. A common mistake is misapplying the square root in the quadratic formula—taking only the positive root without considering both options! Always double-check your calculations and remember that both positive and negative roots are essential for finding all possible solutions!