Is Y=2x^2+3x-2 real roots?

Answer 1

Yes, the quadratic equation Y=2x^2+3x-2 has real roots. To find the roots, we can use the quadratic formula:

x = (-b ± sqrt(b^2-4ac)) / 2a

In this case, a=2, b=3, and c=-2. Substituting these values into the quadratic formula, we get:

x = (-3 ± sqrt(3^2 - 4(2)(-2))) / 2(2)
x = (-3 ± sqrt(25)) / 4
x = (-3 ± 5) / 4

So the roots are:

x = (-3 + 5) / 4 = 1/2
x = (-3 - 5) / 4 = -2

Both of these roots are real numbers, so the answer is yes.

Answer 2

2x^2+3x-2 = (x+2)(2x-1)
so yes, it has roots of -2 and 1/2

Answer 3

You are correct. We can factor the quadratic equation Y=2x^2+3x-2 as (x+2)(2x-1), which means the roots are -2 and 1/2. Both of these roots are real numbers, so the answer is still yes.