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Mathematics · Quadratic Equations · NCERT Examples

Example 3

A complete, independently verified solution for NCERT Example 3.

Mathematics · Chapter 4 · NCERT Examples

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Verified NCERT questions and solutionsSolutions are checked independently and follow the supplied NCERT chapter edition.

NCERT Example

Example 3

factorisation · roots

Find the roots of 2x² − 5x + 3 = 0 by factorisation.

Solution

2x2−5x+3=2x2−2x−3x+32x^2-5x+3=2x^2-2x-3x+3
=2x(x−1)−3(x−1)=(2x−3)(x−1)=2x(x-1)-3(x-1)=(2x-3)(x-1)
2x−3=0orx−1=02x-3=0 \text{or} x-1=0
x=32orx=1x=\frac32 \text{or} x=1

Substitution in the original equation gives zero for both roots.

Final answer

x=1,32x=1, \frac32