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Nature of Roots Video Lecture | Mathematics (Maths) for JEE Main & Advanced
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FAQs on Nature of Roots Video Lecture - Mathematics (Maths) for JEE Main & Advanced
| 1. What is the nature of roots in mathematics? |  |
| 2. How can we determine the nature of roots of a quadratic equation? | |
Ans. To determine the nature of roots of a quadratic equation, we can use the discriminant formula. The discriminant (D) of a quadratic equation ax^2 + bx + c = 0 is given by D = b^2 - 4ac. If the discriminant is positive, the equation will have real and distinct roots. If the discriminant is zero, the equation will have real and equal roots. If the discriminant is negative, the equation will have complex roots.
| 3. Can a quadratic equation have only one root? | |
Ans. Yes, a quadratic equation can have only one root. This occurs when the discriminant of the equation is equal to zero. In such cases, the equation will have real and equal roots, resulting in only one solution.
| 4. What does it mean when a quadratic equation has complex roots? | |
Ans. When a quadratic equation has complex roots, it means that the roots of the equation are not real numbers but involve the imaginary unit, denoted by "i." Complex roots occur when the discriminant of the equation is negative, indicating that the solutions involve complex numbers.
| 5. Can a quadratic equation have no real roots? | |
Ans. Yes, a quadratic equation can have no real roots. This happens when the discriminant of the equation is negative, indicating that the solutions involve complex numbers. In such cases, the equation will not have any real solutions.
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