Answer :
We start with the quadratic function
$$
y = 2x^2 + 9x + 4.
$$
To find its zeros, we need to solve the equation
$$
2x^2 + 9x + 4 = 0.
$$
**Step 1. Identify the coefficients.**
The quadratic equation is in the form
$$
ax^2 + bx + c = 0,
$$
where
$$
a = 2,\quad b = 9,\quad c = 4.
$$
**Step 2. Calculate the discriminant.**
The discriminant $\Delta$ is given by
$$
\Delta = b^2 - 4ac.
$$
Substitute the values of $a$, $b$, and $c$:
$$
\Delta = 9^2 - 4(2)(4) = 81 - 32 = 49.
$$
Since the discriminant is positive, we have two real zeros.
**Step 3. Use the quadratic formula.**
The quadratic formula is
$$
x = \frac{-b \pm \sqrt{\Delta}}{2a}.
$$
Substitute the known values:
$$
x = \frac{-9 \pm \sqrt{49}}{2 \cdot 2} = \frac{-9 \pm 7}{4}.
$$
**Step 4. Compute the two zeros.**
For the first zero, use the $+$ sign:
$$
x = \frac{-9 + 7}{4} = \frac{-2}{4} = -\frac{1}{2}.
$$
For the second zero, use the $-$ sign:
$$
x = \frac{-9 - 7}{4} = \frac{-16}{4} = -4.
$$
Thus, the zeros of the function are
$$
x = -\frac{1}{2} \quad \text{and} \quad x = -4.
$$
**Answer:** Option B.
$$
y = 2x^2 + 9x + 4.
$$
To find its zeros, we need to solve the equation
$$
2x^2 + 9x + 4 = 0.
$$
**Step 1. Identify the coefficients.**
The quadratic equation is in the form
$$
ax^2 + bx + c = 0,
$$
where
$$
a = 2,\quad b = 9,\quad c = 4.
$$
**Step 2. Calculate the discriminant.**
The discriminant $\Delta$ is given by
$$
\Delta = b^2 - 4ac.
$$
Substitute the values of $a$, $b$, and $c$:
$$
\Delta = 9^2 - 4(2)(4) = 81 - 32 = 49.
$$
Since the discriminant is positive, we have two real zeros.
**Step 3. Use the quadratic formula.**
The quadratic formula is
$$
x = \frac{-b \pm \sqrt{\Delta}}{2a}.
$$
Substitute the known values:
$$
x = \frac{-9 \pm \sqrt{49}}{2 \cdot 2} = \frac{-9 \pm 7}{4}.
$$
**Step 4. Compute the two zeros.**
For the first zero, use the $+$ sign:
$$
x = \frac{-9 + 7}{4} = \frac{-2}{4} = -\frac{1}{2}.
$$
For the second zero, use the $-$ sign:
$$
x = \frac{-9 - 7}{4} = \frac{-16}{4} = -4.
$$
Thus, the zeros of the function are
$$
x = -\frac{1}{2} \quad \text{and} \quad x = -4.
$$
**Answer:** Option B.
