1

Problem

Solve the quadratic equation \$2x^2 + 7x + 3 = 0\$ using factors.

2

Step

Write down the given quadratic equation

\$2x^2 + 7x + 3 = 0\$

3

Step

Multiply the coefficient of \$x^2\$ (2) by the constant term (3) to get the product

\$2 * 3 = 6\$

4

Step

Find two numbers that multiply to give 6 and add up to the coefficient of x (7) In this case, the numbers are 6 and 1, because 6 + 1 = 7 and \$6 * 1 = 6 \$.

5

Step

Rewrite the middle term (7x) using these numbers

\$ 2x^2 + 6x + x + 3 \$

6

Step

Group the terms in pairs then simplify the equations

\$ (2x^2 + 6x) + (x + 3) \$
(2x + 1)(x + 3) = 0

7

Step

To find the values of x, we set each factor equal to zero and solve for x then after simplification

x + 3 = 0 or 2x + 1 = 0
x = - 3 or \$x = -(1/2)\$

8

Solution

Therefore, the solutions to the quadratic equation \$2x^2 + 7x + 3 = 0\$ are x = -3 and \$x = -1/2\$

9

Sumup

Please summarize Problem, Clue, Hint, Formula, Steps and Solution

Choices

10

Choice-A

The solutions to the quadratic equations lack precision and are not exact

Wrong \$x = 3 or x = -1/2\$

11

Choice-B

The solutions found for the quadratic equation are both accurate

Correct \$x = -3 or x = -1/2\$

12

Choice-C

The solutions to the quadratic equations lack precision and are not exact

Wrong \$x = 3 or x = 1/2\$

13

Choice-D

The solutions to the quadratic equations lack precision and are not exact

Wrong \$x = -3 or x = 1/2\$

14

Answer

Option

B

15

Sumup

Please summarize choices