Question

3x² – 11x + 6 = 0

Answer 1

Given: 3x² – 11x + 6 = 0

On splitting the middle term –11x as –9x – 2x, we get:

3x² – 9x – 2x + 6 = 0

$\Rightarrow$3x(x – 3) – 2(x – 3) = 0

$\Rightarrow$(x – 3) (3x – 2) = 0

We know that if the product of two numbers is zero, then at least one of them must be zero.

Thus,

x – 3 = 0 or 3x – 2 = 0
$\Rightarrow$ x = 3 or x = $\frac{2}{3}$
Therefore, the solution of the given equation is x = 3, $\frac{2}{3}$.