nature of roots of the quadiratic equation 3X2 - 4x+ 5= 0
b^2 - 4ac = 16 - 4(2)(5) = negative
so there are 2 complex roots.
Why did you title this "trigonometry"?
To determine the nature of the roots of a quadratic equation, we can consider the discriminant (D) of the equation.
For a quadratic equation in standard form: ax^2 + bx + c = 0, the discriminant is given by the formula:
D = b^2 - 4ac
If the discriminant is greater than zero (D > 0), the equation has two distinct real roots.
If the discriminant is equal to zero (D = 0), the equation has two identical real roots.
If the discriminant is less than zero (D < 0), the equation has two complex roots.
Now, let's calculate the discriminant for the given quadratic equation: 3x^2 - 4x + 5 = 0
a = 3, b = -4, c = 5
D = (-4)^2 - 4(3)(5)
D = 16 - 60
D = -44
Since the discriminant is less than zero (D < 0), the given quadratic equation has two complex roots.