1

Problem

Solve the quadratic equation \$2x^2 + 5x - 3 = 0\$.

2

Step

The given equation is

\$2x^2 + 5x - 3 = 0\$

3

Formula

The quadratic formula states that for an equation in the form \$ax^2 + bx + c = 0\$, the solutions for x can be found using the formula: \$x = (-b ± \sqrt (b^2 - 4ac)) / (2a)\$.

4

Hint

Here the a = 2, b = 5 and c = -3.

5

Step

Plug the values in the fromula:

\$x = (-5 ± \sqrt (5^2 - 4 \times 2 \times -3)) / (2 \times 2)\$

\$x = (-5 ± 7) / 4\$

6

Step

This gives us two possible solutions:

\$x_1 = (-5 + 7) / 4, x_2 = (-5 - 7) / 4\$

7

Step

When we take the Positive and negative square roots then after simplified

\$x_1 = (-5 + 7) / 4\$ (or) \$x_2 = (-5 - 7) / 4\$

\$1/2\$ = 0.5 (or) x = -3

8

Solution

Therefore, the solutions to the quadratic equation \$2x^2 + 5x - 3 = 0\$ are x = 0.5 and x = -3.

9

Sumup

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

Choices

10

Choice-A

Both solutions to the quadratic equation are accurate and acceptable

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

11

Choice-B

The solutions for the quadratic equations are not precise

Wrong \$x = 3/2 \$ or x = - 4

12

Choice-C

The solutions for the quadratic equations are not precise

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

13

Choice-D

The solutions for the quadratic equations are not precise

Wrong x = - 0.6 or x = 4

14

Answer

Option

A

15

Sumup

Please summarize choices