FAQs on Basics of Quadratic Equations

Question 1

1. What is a quadratic equation?

Accepted Answer

Ans. A quadratic equation is a second-degree polynomial equation in a single variable with the general form ax^2 + bx + c = 0, where a, b, and c are constants.

Question 2

2. How do you solve a quadratic equation by factoring?

Accepted Answer

Ans. To solve a quadratic equation by factoring, you need to rewrite the equation in the form of (x - p)(x - q) = 0, where p and q are the solutions. Then, set each factor equal to zero and solve for x.

Question 3

3. Can a quadratic equation have more than two solutions?

Accepted Answer

Ans. No, a quadratic equation can have either zero, one, or two solutions. This is because a quadratic equation represents a parabola, which can intersect the x-axis at most two times.

Question 4

4. What is the discriminant of a quadratic equation?

Accepted Answer

Ans. The discriminant of a quadratic equation is the expression b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation. It helps determine the nature of the solutions: positive discriminant indicates two real solutions, zero discriminant indicates one real solution, and negative discriminant indicates two complex solutions.

Question 5

5. Can a quadratic equation have a negative discriminant and still have real solutions?

Accepted Answer

Ans. No, a quadratic equation cannot have a negative discriminant and still have real solutions. If the discriminant is negative, it means the quadratic equation has two complex solutions, which involve imaginary numbers.

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