Question

6x² – 7x – 13 = 0

Answer 1

Given: 6x² – 7x – 13 = 0

On splitting the middle term –7x as 6x – 13x, we get:

6x² + 6x – 13x – 13 = 0

$\Rightarrow$6x(x + 1) – 13(x + 1) = 0

$\Rightarrow$(x + 1) (6x – 13) = 0

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

Thus,

x + 1 = 0 or 6x – 13 = 0
$\Rightarrow$x = –1 or x = $\frac{13}{6}$
Therefore, the solution of the given equation is x = –1, $\frac{13}{6}$.