Class 10 Exam > Class 10 Videos > Mathematics (Maths) Class 10 > How to Find the Discriminant and Determine the Number of Solutions of Quadratic Equations?
How to Find the Discriminant and Determine the Number of Solutions of Quadratic Equations? Video Lecture | Mathematics (Maths) Class 10
FAQs on How to Find the Discriminant and Determine the Number of Solutions of Quadratic Equations? Video Lecture - Mathematics (Maths) Class 10
| 1. How do you find the discriminant of a quadratic equation? |  |
Ans. To find the discriminant of a quadratic equation, you can use the formula Δ = b^2 - 4ac, where Δ represents the discriminant and a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c.
| 2. What does the discriminant indicate about the number of solutions of a quadratic equation? | |
Ans. The discriminant of a quadratic equation helps determine the number of solutions it has. If the discriminant is greater than 0 (Δ > 0), the equation has two distinct real solutions. If the discriminant is equal to 0 (Δ = 0), the equation has exactly one real solution. And if the discriminant is less than 0 (Δ < 0), the equation has no real solutions, but two complex solutions.
| 3. Is it possible for a quadratic equation to have no real solutions? | |
Ans. Yes, it is possible for a quadratic equation to have no real solutions. This occurs when the discriminant is less than 0 (Δ < 0). In such cases, the equation has two complex solutions that involve imaginary numbers.
| 4. How can the discriminant be used to determine the nature of the solutions of a quadratic equation? | |
Ans. The discriminant can be used to determine the nature of the solutions of a quadratic equation. If the discriminant is greater than 0 (Δ > 0), the equation has two distinct real solutions. If the discriminant is equal to 0 (Δ = 0), the equation has exactly one real solution. And if the discriminant is less than 0 (Δ < 0), the equation has no real solutions but two complex solutions.
| 5. Can the discriminant of a quadratic equation be negative? | |
Ans. Yes, the discriminant of a quadratic equation can be negative. When the discriminant is negative (Δ < 0), it indicates that the quadratic equation has no real solutions. However, it still has two complex solutions involving imaginary numbers.
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