What is the square root of the square of a number ? ##\sqrt{a^2} = ?##Wrichik Basu said:
Write the equation without square roots and squares. Do you know what is ##\sqrt{3^2}##? and ##\sqrt{(-3)^2}##? And what is ##\sqrt{a^2}## in general?Wrichik Basu said:
##\sqrt{a^2} = |a|##, that much I know. And the others are both 3.ehild said:
You mean to say that the expression reduces to ## |x|-|x-1|+|x-2|=\sqrt {5}##?ehild said:
Yes, it is correct. Just plot the function, and see, if it can take the value √5, and how many times.Wrichik Basu said:
Right, plot on a number line and... I understood. Thank you, sir.ehild said:
Thank you.ehild said:
A quadratic equation is an algebraic equation of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is a variable. It is called a quadratic equation because the highest power of the variable is 2.
The main difference between a linear and quadratic equation is the highest power of the variable. In a linear equation, the highest power is 1, while in a quadratic equation, the highest power is 2. This means that a quadratic equation can have two solutions, while a linear equation only has one solution.
There are several methods for solving a quadratic equation, including factoring, completing the square, and using the quadratic formula. The most commonly used method is the quadratic formula, which is x = (-b ± √(b^2-4ac)) / 2a. This formula can be used to find the two solutions of any quadratic equation.
Yes, a quadratic equation can have complex solutions. This means that the solutions involve imaginary numbers, such as √-1. Complex solutions occur when the discriminant (b^2-4ac) is negative, indicating that the solutions are not real numbers.
Quadratic equations have many real-life applications, such as in physics, engineering, and finance. They can be used to model the motion of objects, calculate the maximum or minimum value of a function, and solve optimization problems. They are also used in graphing to create parabolas, which can represent various real-world phenomena.