Quadratic Formula/Square Roots Flashcard

The Quadratic Formula is used to find the solutions of a quadratic equation in the form $$ax^2 + bx + c = 0$$ . It is given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ .

The discriminant, given by $$b^2 - 4ac$$ , determines the nature of the roots of a quadratic equation. If it is positive, there are two distinct real roots; if zero, there is one real root; if negative, there are two complex roots.

To solve $$x^2 = 48$$ , take the square root of both sides: $$x = \pm \sqrt{48} = \pm 4\sqrt{3}$$ .

Identify the coefficients a, b, and c from the quadratic equation in the form $$ax^2 + bx + c = 0$$ .

In the Quadratic Formula, 'b' is the coefficient of the linear term $$x$$ in the quadratic equation $$ax^2 + bx + c = 0$$ .

The solution is $$x = \frac{-1 \pm 2i\sqrt{23}}{2}$$ .

The standard form of a quadratic equation is $$ax^2 + bx + c = 0$$ , where a, b, and c are constants and @@a eq 0@@.

To find the roots of a quadratic equation, you can either factor the equation, complete the square, or use the Quadratic Formula.

The sum of the roots is given by $$-\frac{b}{a}$$ and the product of the roots is given by $$\frac{c}{a}$$ .

If the discriminant is zero, it means that the quadratic equation has exactly one real root, also known as a repeated or double root.