Quants Menu

- HCF and LCM
- Number System
- Number Decimals & Fractions
- Surds and Indices
- Divisibility
- Ages
- LCM
- HCF
- Inverse
- Speed Time and Distance
- Work and Time
- Boats and Streams
- Pipes and Cisterns
- Averages
- Allegations and Mixtures
- Ratio and Proportions
- Simple & Compound Interest
- Simple Interest
- Compound Interest
- Percentages
- Profit & Loss
- Successive Discount 1
- Successive Discount 2
- AP GP HP
- Arithmetic Progressions
- Geometric Progressions
- Harmonic Progressions
- Probability
- Permutation & Combination
- Combination
- Circular Permutation
- Geometry
- Heights and Distances
- Perimeter Area and Volume
- Coordinate Geometry
- Venn Diagrams
- Set Theory
- Algebra
- Linear Equations
- Quadratic Equations
- Logarithms
- Clocks
- Calendars
- Clocks and Calendars
- Finding remainder of large powers

PREPINSTA PRIME

# Quadratic Equations Questions and Answers

**Questions on Quadratic Equations **

If you’re looking to master quadratic equations, understanding and practicing various questions on this topic is essential. Quadratic equations are second-degree polynomial equations with the general form ax^2 + bx + c = 0, where ‘a’, ‘b’, and ‘c’ are constants. These equations have two solutions, called roots, which can be found using methods like factoring, completing the square, or using the quadratic formula.

**Methods for finding roots of Quadratic Equation**

The roots or solutions of a quadratic equation are the values of ‘x’ that satisfy the equation, making it true. A quadratic equation can have two real roots, two complex roots, or one real root (in case of a perfect square). The number of roots is determined by the value of the discriminant (Δ) given by:

Δ =** b^{2}-4ac**

- If Δ > 0, the quadratic equation has two distinct real roots.
- If Δ = 0, the quadratic equation has one real root (repeated or equal roots).
- If Δ < 0, the quadratic equation has two complex roots (conjugate pairs).

To find the roots of a quadratic equation, several methods can be used:

**Factoring:**If the equation can be factored, the roots can be directly determined from the factors.**Quadratic Formula:**The quadratic formula is a general method to find the roots of any quadratic equation and is given by:x = \frac{(-b\pm \sqrt{b^{2}-4ac})}{2a}

where the ± sign accounts for the two possible solutions.

**Completing the Square:**This method involves transforming the quadratic equation into a perfect square form, from which the roots can be easily obtained.

**Rules for Quadratic Equations**

- If p+ √q is a root of a quadratic equation, then its other root is p-√q.
- When D ≥ 0, then rx^2+ dx + z can be expressed as a product of two linear factors.
- If α and β are the roots of rx^2+ dx + z, then we can write it as: x^2 – (α + β)x + α β = 0.

### Prime Course Trailer

### Related Banners

Get PrepInsta Prime & get Access to all 200+ courses offered by PrepInsta in One Subscription

## Also Check Out

**Get over 200+ course One Subscription**

Courses like AI/ML, Cloud Computing, Ethical Hacking, C, C++, Java, Python, DSA (All Languages), Competitive Coding (All Languages), TCS, Infosys, Wipro, Amazon, DBMS, SQL and others

- Algebra – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Linear Equations – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts

- Algebra –

Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts - Linear Equations –

Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts