Roots of a Quadratic Equation

What's the question

Quadratic equation always have two roots.

Wr can find the roots in anyone of the following ways.

1. Factorizing.

2. Quadratic formula

3. Completing the Square.

Roots can be real, equal and imaginary depends upon equation.

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The other possible method is to use complete the square.

x=4 and x=-1 as the roots for x2 - 3x - 4 = 0 as this can be factorised into (x-4)(x+1)

It seems like you're discussing the roots of a quadratic equation, which are the values of x that satisfy the equation when plugged in.

The roots can indeed be found using various methods, including the quadratic formula or calculators designed for this purpose.

The derivative of a quadratic equation, however, typically refers to the derivative of the equation itself concerning x, not its roots.

The derivative of a quadratic equation \(ax^2 + bx + c = 0\) with respect to x is \(2ax + b\).

You can find the roots of a quadratic equation with many different methods:

• Quadratic equation; namely x = [-b+-sqrt(b^2-4ac)] / 2a
• Factorising; e.g. x^2+7x+12=0 therefore (x+4)(x+3) = 0, so either x+4=0 or x+3=0, therefore x=-4 or -3
• Completing the square; e.g. x^2+2x-5 = 0, therefore (x+1)^2-5-1 = 0; (x+1)^2-6 = 0; (x+1)^2=6; (x+1) = +-sqrt(6); x = -1 +- sqrt(6)
• Graphically; e.g. if ax^2 + bx + c = 0, you can graph f(x) = ax^2 + bx + c, and find solutions for x where f(x) = 0.

The derivative of a quadratic equation (not the quadratic formula) results in a linear equation. For instance, for the quadratic equation ��2+��+�=0

ax2

+bx+c=0, its derivative is 2��+�

2ax+b.

The roots of a quadratic equation are the values of �

x that make the equation equal to zero. In your example, for the quadratic equation �2−3�−4=0

x2

−3x−4=0, the roots are �=−1

x=−1 and �=4

x=4

The quadratic formula x=2a

−b±b2

−4ac

If you have further questions or specific points you'd like clarification on, feel free to ask!

You can use quadratic formula or by factorisation.

complete the square