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FAQs on Sample Solution Paper 7 - Math, Class 11 - Mathematics (Maths) Class 11 - Commerce

1. What is the quadratic formula?
Ans. The quadratic formula is a formula used to find the roots (or solutions) of a quadratic equation. It is given by x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
2. How is the discriminant related to the solutions of a quadratic equation?
Ans. The discriminant is a term that appears under the square root in the quadratic formula. It is calculated as b^2 - 4ac. The discriminant determines the nature of the solutions of a quadratic equation. If the discriminant is positive, the equation has two distinct real solutions. If it is zero, the equation has one real solution (a double root). And if the discriminant is negative, the equation has two complex conjugate solutions.
3. Can a quadratic equation have no solutions?
Ans. Yes, a quadratic equation can have no solutions. This occurs when the discriminant is negative, meaning the square root in the quadratic formula would involve imaginary numbers. In other words, if b^2 - 4ac < 0, the equation has no real solutions. However, it is still possible to find complex solutions to the equation.
4. How can I determine the nature of the solutions without solving the quadratic equation?
Ans. You can determine the nature of the solutions of a quadratic equation by examining the discriminant. If the discriminant is positive, the equation has two distinct real solutions. If it is zero, the equation has one real solution. And if the discriminant is negative, the equation has two complex conjugate solutions.
5. Can the quadratic formula be used to solve any type of equation?
Ans. No, the quadratic formula can only be used to solve quadratic equations, which are equations of the form ax^2 + bx + c = 0. It cannot be used to solve equations of higher degrees, such as cubic or quartic equations. For those types of equations, different formulas and methods are used.
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