Consider f(x) = x2 + px + 45,
Let one root of the given quadratic polynomial is α
Other root of the given quadratic polynomial is β
Sum of the roots
Product of the roots
According to the question:
squared difference of the zeros = 144
(α - β)2 = 144
Apply the formula (x - y)2 = x2 + y2 - 2xy
Apply the formula (x+y)2 = x2 + y2 + 2xy
⇒ (-p)2 - 4× 45 = 144
⇒ p2 - 4× 45 = 144
⇒ p2 - 180= 14
⇒ p2 = 144 + 180
⇒ p2 = 324
⇒ p = ±18