Solve −2x2 +3x − 9 = 0. (2 points)
Select one:
a. x equals quantity of 3 plus or minus 3i square root of 7 all over 4
b. x equals quantity of 3 plus or minus 9i square root of 7 all over 4
c. x equals quantity of negative 3 plus or minus 3i square root of 7 all over 4
d. x equals quantity of negative 3 plus or minus 9i square root of 7 all over 4

Respuesta :

Answer:

Option A

Step-by-step explanation:

We have to find the solution of [tex]-2x^{2}+3x-9=0[/tex]

By quadratic formula

[tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex]

[tex]=\frac{-3\pm \sqrt{(3)^{2}-4(-2)(-9)}}{2(-2)}[/tex]

[tex]=\frac{-3\pm \sqrt{9-72}}{-4}[/tex]

[tex]=\frac{3\mp \sqrt{-63}}{4}[/tex]

[tex]\frac{3\mp 3\sqrt{-7}}{4}=[\frac{3\mp 3i\sqrt{7}}{4}][/tex]

Option A is the answer.

Answer:

Option A) x equals quantity of 3 plus or minus 3i square root of 7 all over 4.

Step-by-step explanation:

We are given the quadratic equation:

[tex]-2x^2 +3x - 9 = 0[/tex]

To find the solution to this quadratic equation, we use the quadratic formula:

[tex]ax^2 + bx + c = 0\\\\x = \displaystyle\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\\text{where a is the coefficient of } x^2\text{, b is the coefficient of x and c is the constnt term of the eqution.}[/tex]

Putting the value of a, b and c in the quadratic formula:

[tex]a = -2\\b = 3\\c = -9\\\\x = \displaystyle\frac{-3 \pm \sqrt{3^2 - 4(-2)(-9)}}{2(-2)}\\\\x = \frac{-3 \pm \sqrt{-63} }{-4}\\\\x = \frac{-3 \pm 3i\sqrt7}{-4}\\\\x = \frac{3 \mp3i\sqrt7}{4}[/tex]

Hence, the correct option is option A) x equals quantity of 3 plus or minus 3i square root of 7 all over 4.

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