Question

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

Answer 1

Answer:

1. 2x²-5x+3=0
2. 2x²-2x-3x+3
3. 2x(x-1)-3(x-1)
4. (2x-3)(x-1)

So the roots of the equation are 3/2 and 1

Answer 2

Answer:

$\bf{Solution:-}$

Let us first spilt the middle term $\bf{ –5x as –2x –3x}$ [because $\bf{ (–2x) × (–3x) = 6x² = (2x²) × 3}$ ].

So, $\bf{2x²–5x+3=2x²–2x–3x+3=2x(x–1)–3(x–1)=(2x–3)(x–1)}$

Now, $\bf{2x²–5x+3=0}$ can be rewritten as $\bf{ (2x–3)(x–1)=0 }$

So, the value of x for which $\bf{2x²–5x+3=0}$ are the same for which $\bf{ (2x–3)(x–1)=0, }$

i.e., either 2x–3=0 gives x=³/₂ and x–1=0 gives x=1.

So, $\bf{x = ³/₂}$ and $\bf{x = 1}$ are the solution of the equation.

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

$\bf{Verify}$ that these are the roots of the given equation.