Question

x² – 17x + 60 = 0

Answer 1

Given: x² – 17x + 60 = 0

On splitting the middle term –17x as – 12x – 5x, we get:

x² – 12x – 5x + 60 = 0

$\Rightarrow$x(x – 12) – 5(x – 12) = 0

$\Rightarrow$(x – 12) (x – 5) = 0

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

Thus,

x – 12 = 0 or x – 5 = 0

$\Rightarrow$ x = 12 or x = 5

Therefore, the solution of the given equation is x = 12, 5.