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Basics: Quadratic Equations Video Lecture | Crash Course: Class 10

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FAQs on Basics: Quadratic Equations Video Lecture - Crash Course: Class 10

1. What is a quadratic equation?
Ans. A quadratic equation is a polynomial equation of degree 2, which means the highest power of the variable is 2. It can be written in the form of ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.
2. How do you solve a quadratic equation?
Ans. To solve a quadratic equation, we can use various methods such as factoring, completing the square, or using the quadratic formula. In factoring, we try to factorize the equation into two binomial expressions. Completing the square involves transforming the equation into a perfect square trinomial. The quadratic formula is a handy formula that gives the solutions directly as x = (-b ± √(b^2-4ac)) / (2a).
3. What are the roots of a quadratic equation?
Ans. The roots of a quadratic equation are the values of x that satisfy the equation and make it true. In other words, they are the values of x for which the quadratic equation equals zero. A quadratic equation can have zero, one, or two distinct roots depending on the discriminant (b^2-4ac) of the equation. If the discriminant is positive, there are two distinct real roots. If it is zero, there is one real root (also called a repeated root). If the discriminant is negative, there are no real roots, but there will be two complex roots.
4. Can a quadratic equation have only one root?
Ans. Yes, a quadratic equation can have only one root. This happens when the discriminant of the equation is zero. When the discriminant is zero, the quadratic equation has a repeated root. Geometrically, this means that the graph of the quadratic equation is a perfect square and the parabola touches the x-axis at only one point.
5. What is the importance of quadratic equations in real life?
Ans. Quadratic equations have various real-life applications. They are used in physics to describe the motion of objects under the influence of gravity or other forces. They are also used in engineering to solve problems related to optimization, projectile motion, and structural analysis. In economics, quadratic equations are used to model revenue, cost, and profit functions. Additionally, quadratic equations are also used in computer graphics, architecture, and many other fields. Understanding quadratic equations is essential in solving real-world problems and making informed decisions.
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