Question

What are the roots of x in -10x2 + 12x − 9 = 0?

Answer 1

x = 3[2 + i√-6]/10 or x = 3[2 - i√-6]/10

Explanation:

Formula

Solution of a quadratic equation ax² + bx + c = 0

x = [-b ± √(b² - 4ac)]/2a

To find the solution

It is given that,

-10x² + 12x - 9 = 0

here a = -10, b = 12 and c = -9

x = [-b ± √(b² - 4ac)]/2a

= [-12 ± √(12² - 4* -10 * -9)]/2 * -10

= [-12 ± √(144 - 360)]/-20

=[12 ± √-216]/20

= [12 ± i6√-6]/20

= [6 ± i3√-6]/10

= 3[2 ± i√-6]/10

x = 3[2 + i√-6]/10 or x = 3[2 - i√-6]/10

Answer 2

`x_1=(3(2+i√(6)))/(10)`

`x_2=(3(2-i√(6)))/(10)`

Explanation:

Use the Quadratic formula:

`x=(-b\±√(b^2-4ac))/(2a)`

You can identify that, in this case:

`a=-10\\b=12\\c=-9`

Now you need to substitute these values into the formula:

`x=(-12\±√(12^2-4(-10)(-9)))/(2(-10))`

`x=(-12\±√(-216))/(-20)`

Remember that:

`i=√(-1)`

Therefore,rewriting and simplifying, you get:

`x=(-12\±6i√(6))/(-20)`

`x=(-6(2\±i√(6)))/(-2(10))`

`x=(3(2\±i√(6)))/(10)`

Then, you get the following roots:

`x_1=(3(2+i√(6)))/(10)`

`x_2=(3(2-i√(6)))/(10)`