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Quadratic Equations : Algebra Video Lecture | Crash Course for CAT

790 videos|33 tests

FAQs on Quadratic Equations : Algebra Video Lecture - Crash Course for CAT

1. What is a quadratic equation?
Ans. A quadratic equation is a polynomial equation of the second degree, where the highest power of the variable is 2. It can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.
2. How can I solve a quadratic equation?
Ans. There are several methods to solve a quadratic equation. The most common methods are factoring, using the quadratic formula, or completing the square. Factoring involves finding two binomials that multiply to give the quadratic expression. The quadratic formula provides a direct way to find the solutions of a quadratic equation. Completing the square is a method of rewriting the quadratic equation in a perfect square form to solve it.
3. What is the discriminant of a quadratic equation?
Ans. The discriminant of a quadratic equation is the expression b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0. It helps determine the nature of the solutions of the quadratic equation. If the discriminant is positive, the equation has two distinct real solutions. If the discriminant is zero, the equation has one real solution. If the discriminant is negative, the equation has two complex solutions.
4. Can a quadratic equation have no solutions?
Ans. Yes, a quadratic equation can have no solutions. This happens when the discriminant is negative, indicating that the equation has two complex solutions. Complex solutions involve imaginary numbers and do not lie on the real number line. In such cases, the quadratic equation does not intersect the x-axis and has no real solutions.
5. What are the applications of quadratic equations?
Ans. Quadratic equations have various applications in real-life situations. They are used in physics to study motion, such as calculating the trajectory of a projectile. They are also used in engineering to model and solve problems related to structures, electrical circuits, and fluid dynamics. Additionally, quadratic equations find applications in economics, finance, computer graphics, and optimization problems.
790 videos|33 tests
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