Question

Find the solutions to the equation below. Check all that apply.

A. x = 4
B. x = 7
C. x = -1
D. x = 2
E. x = -3
F. x = 3
2x² + 7x + 3 = 0

Answer 1

A. x = 4

C. x = -1

Step-by-step explanation:

To find the solutions to the quadratic equation

`2�2+7�+3=02x 2 +7x+3=0`, we can use the quadratic formula:

`�=−�±�2−4��2�x= 2a−b± b 2 −4ac`

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, where

`�a, �b, and �`

c are coefficients of the quadratic equation

`��2+��+�=0ax 2 +bx+c=0.`

In this case,

`�=2a=2, �=7b=7, and �=3`

c=3. Plugging these values into the quadratic formula gives us two solutions:

`�=−7+72−4(2)(3)2(2)≈−1`

(Solution C)

`x= 2(2)−7+ 7 2 −4(2)(3)`

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≈−1(Solution C)

`�=−7−72−4(2)(3)2(2)≈4`

(Solution A)

`x= 2(2)−7− 7 2 −4(2)(3)​`

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≈4(Solution A)

Therefore, the correct solutions are A. x = 4 and C. x = -1. These values satisfy the original quadratic equation

`2�2+7�+3=02x 2 +7x+3=0.`