Question

Select the correct answer.
What are the roots of this quadratic equation?

Answer 1

Option A

Explanation:

I used the quadratic equation:

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

Answer 2

The roots of the quadratic equation -10x² + 12x - 9 = 0 are complex and can be found using the quadratic formula. The final solutions are x = −1/2 ± (3*sqrt(6)/10)i, which indicates that there are no real roots for this equation.

To find the roots of the quadratic equation -10x² + 12x - 9 = 0, we can use the quadratic formula, which is x = −b ± √(b² - 4ac) / (2a), where a, b, and c are the coefficients of the terms in the quadratic equation ax² + bx + c = 0.

For this equation, a = -10, b = 12, and c = -9. Plugging these values into the formula, we get:

x = −12 ± √((12)² - 4(-10)(-9)) / (2(-10))

x = −12 ± √(144 - 360) / −20

x = −12 ± √(−216) / −20

Since we have a negative number under the square root, the equation has complex roots. The square root of −216 can be written as sqrt(216) times i, where i is the imaginary unit. So:

x = (12 ± sqrt(216) * i) / −20

Simplifying further, we find that sqrt(216) is equal to sqrt(36*6), which simplifies to 6*sqrt(6). The final solution is:

x = −1/2 ± (3*sqrt(6)/10)i