# If the squared difference of the zeros of the quadratic polynomial is equal to 144, find the value of p.

Consider ,

Let one root of the given quadratic polynomial is

Other root of the given quadratic polynomial is β

Sum of the roots = = = = -p

Product of the roots = = = 45

According to the question: squared difference of the zeros = 144

Apply the formula (x-y)2 = x2 + y2 - 2xy

Apply the formula (x+y)2 = x2 + y2 + 2xy

= 144

⇒ (-p)2  - 4× 45 = 144

⇒ p2  - 4× 45 = 144

⇒ p2  - 180= 144

⇒ p2 = 144 + 180

⇒ p2 = 324

⇒ p = ±18

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