Question

What are the zeros of the function y = 2x^2 + 7x + 3?

A. x = -3, x = 1
B. x = -3, x = 3
C. x = -3/2, x = -2
D. x = -3, x = 2

Answer 1

To find the zeros of the function y = 2x^2 + 7x + 3, we solve the quadratic equation by using the quadratic formula. The solution reveals the zeros to be x = -1/2 and x = -3, which corresponds to option C.

Correct answer is option C.

Step-by-step explanation:

The student is asking to find the zeros of the quadratic function y = 2x^2 + 7x + 3. To find the zeros, we need to solve for x when y is equal to zero.

Setting the function equal to zero gives:

2x^2 + 7x + 3 = 0

This is a quadratic equation in the form of ax^2 + bx + c = 0. We can either factor the quadratic, if possible, or use the quadratic formula:

x = −b ± √(b^2 - 4ac) / (2a)

For our equation:

• a = 2
• b = 7
• c = 3

The discriminant (b^2 - 4ac) is:
(7)^2 - 4(2)(3) = 49 - 24 = 25

Since the discriminant is a perfect square, we can find two real solutions for x:

x = (-7 ± √25) / (2 * 2)

The two solutions are:

x = (-7 + 5) / 4 = -2 / 4 = -1/2

x = (-7 - 5) / 4 = -12 / 4 = -3

Therefore, the zeros of the function are x = -1/2 and x = -3.

The correct answer is option C: x = -3/2, x = -2