Question

If the squared difference of the zeros of the quadratic polynomial f(x) = x² + px + 45 is equal to 144, find the value of p.

Answer 1

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