Question

Discriminat and types of root

y=2x^2-6x+3

Answer 1

The given equation is a quadratic equation with a discriminant of 12, indicating two distinct real roots.

Step-by-step explanation:

The given equation is a quadratic equation in the form y = ax^2 + bx + c. In this equation, a = 2, b = -6, and c = 3.

To find the discriminant, we can use the formula: D = b^2 - 4ac.

Substituting the values into the formula, D = (-6)^2 - 4(2)(3) = 36 - 24 = 12.

The discriminant of 12 indicates that the equation has two real and distinct roots.

The types of roots can be determined by the discriminant as follows:

• If D > 0, the equation has two distinct real roots.
• If D = 0, the equation has one real root (a repeated root).
• If D < 0, the equation has two complex conjugate roots (non-real roots).

Since the discriminant is positive (D > 0), the given equation has two distinct real roots.