UPSC > CSAT Preparation > Practice Questions: Quadratic Equations
Practice Questions: Quadratic Equations Video Lecture - CSAT Preparation - UPSC
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FAQs on Practice Questions: Quadratic Equations Video Lecture - CSAT Preparation - UPSC
| 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 ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.
| 2. How do you solve a quadratic equation? | |
Ans. There are several methods to solve a quadratic equation, including factoring, completing the square, and using the quadratic formula. Factoring involves finding two binomials whose product is equal to the quadratic equation. Completing the square involves manipulating the equation to express it as a perfect square trinomial. The quadratic formula is a general formula that can be used to find the solutions of any quadratic equation.
| 3. Can a quadratic equation have more than two solutions? | |
Ans. No, a quadratic equation can have at most two solutions. This is because a quadratic equation represents a parabola, which can intersect the x-axis at most two times. The solutions can be real or complex, but the number of solutions remains limited to two.
| 4. What are the discriminant and how is it used in solving quadratic equations? | |
Ans. The discriminant is a term used in quadratic equations to determine the nature of the solutions. It is calculated by taking the square root of b^2 - 4ac, where a, b, and c are the coefficients 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 repeated real solution. If the discriminant is negative, the equation has two complex solutions.
| 5. Are there any real-life applications of quadratic equations? | |
Ans. Yes, quadratic equations have numerous real-life applications. They can be used to model the motion of objects in freefall, determine the maximum or minimum points of a parabolic curve, solve problems related to projectile motion, and analyze the profit and cost functions in business and economics. Additionally, quadratic equations are prevalent in fields like physics, engineering, and computer graphics.
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