Question

2m² + 19m + 30 = 0

Answer 1

Given: 2m² + 19m + 30 = 0

On splitting the middle term 19m as 4m + 15m, we get:

2m² + 19m + 30 = 0

$\Rightarrow$2m² + 4m + 15m + 30 = 0

$\Rightarrow$2m(m + 2) + 15(m + 2) = 0

$\Rightarrow$(m + 2) (2m + 15) = 0

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

Thus,

m + 2 = 0 or 2m + 15 = 0

$\Rightarrow$m = –2 or m = $-\frac{15}{2}$
Therefore, the solution of the given equation is m = –2, $-\frac{15}{2}$.