Evaluate the discriminant for each equation. Then use it to determine the number and type of solutions. 16x² +3 = -26x

Key Concepts

Discriminant

The discriminant is a key component of the quadratic formula, given by the expression b² - 4ac in the standard form of a quadratic equation ax² + bx + c = 0. It helps determine the nature of the roots of the equation. If the discriminant is positive, there are two distinct real solutions; if it is zero, there is exactly one real solution; and if it is negative, there are two complex solutions.

Quadratic Equations

A quadratic equation is a polynomial equation of degree two, typically expressed in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. These equations can represent various real-world phenomena and are fundamental in algebra. Solving them often involves factoring, completing the square, or using the quadratic formula.

Standard Form

The standard form of a quadratic equation is a way of writing the equation as ax² + bx + c = 0. This format is essential for applying the quadratic formula and calculating the discriminant. To analyze the given equation, it must first be rearranged into this standard form, allowing for the identification of coefficients a, b, and c necessary for further calculations.