Quadratic Equations | Chapter 4 | Class 10th | Quick Revision (22-23) | NCERT | Maths

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Dear students, In this chapter we will learn about Quadratic Equations.

Below ⬇️ are the tutorial notes and videos.

QUADRATIC EQUATIONS

The polynomial of degree two is called quadratic polynomial and equation corresponding to a quadratic polynomial P(x) is called a quadratic equation in variable x.

Thus, P(x) = ax^2+ bx + c =0, a ≠ 0, a, b, c ∈ R is known as the standard form of quadratic equation.

There are two types of quadratic equation.

(i) Complete quadratic equation : The equation ax^2 + bx + c =0 where a ≠ 0, b ≠ 0,c ≠ 0 

(ii) Pure quadratic equation : An equation in the form of ax^2= 0, a ≠ 0, b = 0, c = 0



Question: Find the roots of the equation 2x^2 – 5x + 3 = 0, by factorisation. 

Solution : Let us first split the middle term – 5x as –2x –3x [because (–2x) × (–3x) =

6x^2= (2x^2) × 3].

So, 2x^2–5x+3=2x^2 –2x–3x+3=2x(x–1)–3(x–1)=(2x–3)(x–1)

Now,2x^2 –5x+3=0 can we written  as (2x–3)(x–1)=0.

So, the values of x for which 2x^2 –5x+3=0 are the same for which (2x–3)(x–1)=0, i.e., 

either 2x – 3 = 0 or x – 1 = 0.

Now,2x–3=0 gives x=32 and x–1=0 gives x=1. So, x = 32 and x = 1 are the solutions of the equation.

In other words,1and 32 are the roots of the equation 2x^2–5x+3=0.
















For any doubt don’t hesitate to comment below ⬇️ or in YouTube.

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