Respuesta :

✨ Using factorisation method ✨

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[tex] \begin{cases}\tt \Large \orange\rightarrow \: \: 2 {x}^{2} \: + \: x \: - \: 6 \: = \: 0 \\ \\\tt \Large \orange\rightarrow \: \:2 {x}^{2} \: + \: 4x \: - \: 3x \: - \: 6 \: = \: 0 \\ \\ \tt \Large \orange\rightarrow \: \:2x(x + 2) \: - 3(x + 2) \: = \: 0 \\ \\ \tt \Large \orange\rightarrow \: \:(2x - 3) \quad \: (x + 2) \: = \: 0 \\ \\ \tt \Large \orange\rightarrow \: \:(2x - 3) = 0 \quad \: (x + 2) = 0 \\ \\ \tt \Large \orange\rightarrow \: \:2x \: = \: 3 \quad;\quad \: x \: = \: - 2 \\ \\ \rm \Large \orange\rightarrow \: \:x \: = \: \frac{3}{2} \quad ;\quad \: x \: = \: - 2 \\ \end{cases}[/tex]

Hence , option d is the correct answer

ajeigbeibraheem

The solution of x in the quadratic equation is (-2, 3/2)

What is a quadratic equation?

A quadratic equation is an algebraic expression whose variable is raised to the maximum power of a second degree.

From the given information, we have the quadratic equation:

[tex]\mathbf{2x^2 + x - 6 = 0}[/tex]

So, we are going to look for two numbers whose multiplication is equal to (-12) and;

The addition and subtraction of those two numbers will be equal to 1.

  • The numbers are: +4 and -3

Then, the quadratic equation can now be written as:

2x² + 4x -3x - 6 = 0

2x(x + 2) -3(x + 2) = 0

(2x - 3) (x + 2) = 0

2x -3 = 0     or      x + 2 = 0

2x = 3         or       x = -2

x = 3/2        or       x = -2

Learn more about quadratic equation here:

https://brainly.com/question/1214333

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