Find the roots of the equation 2x2 – 5x + 3 = 0, by factorisation.

1.	Find the roots of the equation 2x2 – 5x + 3 = 0, by factorisation.
Answer» Let us first split the middle term – 5x as –2x –3x [because (–2x) × (–3x) = 6x² = (2x²) × 3]. So, 2x² – 5x + 3 = 2x² – 2x – 3x + 3 = 2x (x – 1) –3(x – 1) = (2x – 3)(x – 1) Now, 2x² – 5x + 3 = 0 can be rewritten as (2x – 3)(x – 1) = 0. So, the values of x for which 2x² – 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=3/2 and x – 1 = 0 gives x = 1. So, x=3/2 and x = 1 are the solutions of the equation. In other words, 1 and 3/2 are the roots of the equation 2x² – 5x + 3 = 0. Verify that these are the roots of the given equation.

Answer»

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

6x² = (2x²) × 3].

So, 2x² – 5x + 3 = 2x² – 2x – 3x + 3 = 2x (x – 1) –3(x – 1) = (2x – 3)(x – 1)

Now, 2x² – 5x + 3 = 0 can be rewritten as (2x – 3)(x – 1) = 0.

So, the values of x for which 2x² – 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=3/2 and x – 1 = 0 gives x = 1.

So, x=3/2 and x = 1 are the solutions of the equation.

In other words, 1 and 3/2 are the roots of the equation 2x² – 5x + 3 = 0.

Verify that these are the roots of the given equation.

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