Question

What are the roots of x in -10x^2 + 12x - 9 = 0?

a) x = -1, x = 9/10
b) x = -3/5, x = 3/2
c) x = -2/3, x = 3/5
d) x = -3/10, x = 1/3

Answer 1

The roots of the quadratic equation -10x^2 + 12x - 9 = 0 do not exist in the set of real numbers.

Step-by-step explanation:

To find the roots of the quadratic equation -10x^2 + 12x - 9 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values a = -10, b = 12, c = -9 into the formula, we get:

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

Simplifying further, we have:

x = (-12 ± √(144 - 360)) / -20

x = (-12 ± √(-216)) / -20

Since the discriminant (b^2 - 4ac) is negative, there are no real roots. Therefore, the answer is none of the given options.