Find the root of the following quadratic equations by the factorisation method: 25x2-x-35 = 0 - Mathematics

Sum

Find the root of the following quadratic equations by the factorisation method:

2/5x^2 - x - 3/5 = 0

Solution

Given equation is 2/5x^2 - x - 3/5 = 0

On multiplying by 5 on both sides, we get

⇒ 2x^2 - 5x - 3 = 0

2x^2 - (6x - x) - 3 = 0  ....[By splitting middle term]

⇒ 2x^2 - 6x + x - 3 = 0

⇒ 2x(x - 3) + 1(x - 3) = 0

Now (x - 3)(2x + 1) = 0

x - 3 = 0

⇒ x = 3

And 2x + 1 = 0

⇒ x = - 1/2

Hence the roots of the equation2x^2 - 5x - 3 = 0 are - 1/2 and 3.

Concept: Solutions of Quadratic Equations by Factorization
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NCERT Mathematics Exemplar Class 10