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Quadratic Equation - 4 Video Lecture - Class 10 ICSE
FAQs on Quadratic Equation - 4
| 1. What is a quadratic equation? |  |
Ans. A quadratic equation is a polynomial equation of degree two, typically expressed in the standard form as ax² + bx + c = 0, where 'a', 'b', and 'c' are constants, and 'a' is not equal to zero. The solutions to this equation can be found using various methods such as factoring, completing the square, or the quadratic formula.
| 2. How can the roots of a quadratic equation be determined? | |
Ans. The roots of a quadratic equation can be determined using the quadratic formula, which is given as x = (-b ± √(b² - 4ac)) / (2a). Here, 'b² - 4ac' is known as the discriminant. The nature of the roots can be inferred from the discriminant: if it is positive, there are two distinct real roots; if it is zero, there is one real root; and if it is negative, the roots are complex and not real.
| 3. What is the significance of the discriminant in a quadratic equation? | |
Ans. The discriminant, represented by the expression b² - 4ac, is significant because it helps determine the nature of the roots of the quadratic equation. It informs us about the number and type of solutions: a positive discriminant indicates two distinct real roots, a zero discriminant indicates one real root (a repeated root), and a negative discriminant indicates two complex roots.
| 4. Can you explain how to factor a quadratic equation? | |
Ans. To factor a quadratic equation of the form ax² + bx + c, one looks for two numbers that multiply to 'ac' (the product of 'a' and 'c') and add up to 'b'. Once the appropriate numbers are identified, the equation can be rewritten in a factored form as a(x + p)(x + q), where 'p' and 'q' are the numbers found. This method is often most straightforward when 'a' is equal to 1.
| 5. What are some real-life applications of quadratic equations? | |
Ans. Quadratic equations have numerous real-life applications, such as in physics for projectile motion, in business for profit maximisation and cost minimisation, and in engineering for optimising areas and volumes. They can also model various relationships in nature, economics, and other fields where relationships between variables can be represented by a parabolic curve.
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Apr 18, 2026 Last updated
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