# RD Sharma Solutions Class 11 Quadratic Equations

## RD Sharma Solutions Class 11 Chapter 14

The general form of a quadratic equation is $ax^{2}\;+\; bx \;+\;c\;=\;0$

(Where a, b, c are real and a is not equal to 0)

Let $\alpha$ and $\beta$ be the roots of this quadratic equation.

Therefore, $\alpha \;+ \;\beta\;=\; \frac{-b}{a}$ and  $\alpha \beta\;=\; \frac{c}{a}$

Also, $\alpha \;=\;\frac{-b+\sqrt{b^{2}-4ac}}{2a}$ and $\beta \;=\;\frac{-b-\sqrt{b^{2}-4ac}}{2a}$

The nature of roots depends on the following cases:

Case 1: $b^{2}-4ac\;>\; 0$

When the values of discriminant are positive then the roots of the quadratic equation are real and unequal.

Case 2: $b^{2}-4ac\;=\; 0$

When the value of discriminant is 0 then the roots of the quadratic equation are real and equal.

Case 3: $b^{2}-4ac\;<\; 0$<

When the values of discriminant are negative then the roots of the quadratic equation are unequal and imaginary.

RD Sharma Solutions for Class 11th maths Quadratic Equation will help you to understand the different techniques of solving quadratic equations in a very easy and simplified way. Learn all the important concepts related to quadratic equations in detail with complete exercise wise solved RD Sharma Solutions to answer complex questions asked in highly competitive exams like JEE Mains and JEE Advanced quickly and accurately.

#### Practise This Question

A cake recipe says that you need to put 3 bowls of sugar for every 5 bowls of flour. However, for an upcoming party, you need a bigger cake. If you use 20 bowls of flour, how much sugar is required?