Question

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

Answer 1

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

Explanation:

We are given the quadratic equation:

`-2x^2 +3x - 9 = 0`

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

`ax^2 + bx + c = 0\\\\x = \displaystyle(-b \pm √(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.}`

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

`a = -2\\b = 3\\c = -9\\\\x = \displaystyle(-3 \pm √(3^2 - 4(-2)(-9)))/(2(-2))\\\\x = (-3 \pm √(-63) )/(-4)\\\\x = (-3 \pm 3i\sqrt7)/(-4)\\\\x = (3 \mp3i\sqrt7)/(4)`

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

Answer 2

Option A

Explanation:

We have to find the solution of
`-2x^(2)+3x-9=0`

By quadratic formula

`x=\frac{-b\pm \sqrt{b^(2)-4ac}}{2a}`

`=\frac{-3\pm \sqrt{(3)^(2)-4(-2)(-9)}}{2(-2)}`

`=(-3\pm √(9-72))/(-4)`

`=(3\mp √(-63))/(4)`

`(3\mp 3√(-7))/(4)=[(3\mp 3i√(7))/(4)]`

Option A is the answer.