Practice Questions on Quadratic Equation
1. What is the standard form of a quadratic equation?
- ax2 + bx + c = 0
- y = mx + b
- a2 + b2 = c2
- x + y = 1
2. In the quadratic equation ax2 + bx + c = 0, what does ‘a’ represent?
- Linear coefficient
- Constant term
- Quadratic coefficient
- Discriminant
3. What is the discriminant of a quadratic equation ax2 + bx + c = 0?
- b2 – 4ac
- 2ab – c
- a2 + b2
- 2b – a
4. When discriminant is greater than zero in a quadratic equation, what can be said about the solutions?
- No real solutions
- One real solution
- Two distinct real solutions
- Infinite solutions
5. Which method can be used to solve a quadratic equation when the discriminant is zero?
- Factoring
- Completing the square
- Quadratic formula
- Graphing
6. If a quadratic equation has complex roots, what can be said about the discriminant?
- It is greater than zero
- It is less than zero
- It is equal to zero
- It can be any value
7. What is the vertex form of a quadratic equation?
- y = ax2 + bx + c
- y = a(x – h)2 + k
- y = mx + b
- x = -b ± √(b2 – 4ac) / 2a
8. In the quadratic formula, what does the term ± represent?
- Plus or minus
- Multiply
- Divide
- Square root
9. If the quadratic equation is written in the form y = a(x – h)2 + k, what do the values h and k represent?
- x-intercepts
- y-intercepts
- Vertex coordinates
- Quadratic coefficient
10. What is the relationship between the roots of a quadratic equation and the coefficients in the equation?
- There is no relationship
- Roots are the opposite of the coefficients
- Roots are the reciprocals of the coefficients
- Roots are related to the discriminant
Quadratic Equations: Formula, Method and Examples
A Quadratic equation is a second-degree equation that can be represented as ax2 + bx + c = 0. In this equation, x is an unknown variable, a, b, and c are constants, and a is not equal to 0. To solve it, you can use methods such as factoring, completing the square, or the quadratic formula. Each method helps find the values of x that satisfy the equation.
Let’s learn how to solve Quadratic Equations using different methods in detail.
Table of Content
- What is Quadratic Equation?
- Quadratic Equation Standard Form
- Quadratic Equation Examples
- Roots of Quadratic Equation
- Quadratic Equations Formula
- Nature of Roots
- Discriminant
- Sum of Roots in Quadratic Equation
- Product of Roots in Quadratic Equation
- Writing Quadratic Equations using Roots
- How to Solve Quadratic Equation?
- Factorization Method
- Completing Square Method
- Graph Method
- Quadratic Equations Having Common Roots
- Maximum and Minimum Value of Quadratic Equation
- Quadratic Equation Sign Convention
- Solved Examples on Quadratic Equation
- Practice Questions on Quadratic Equation
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