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Let ∝ and β be the zeroes of the given quadratic polynomial.
∴∝ + β = – p and ∝β = 45 ...(1)
Given, (∝ – β)2 = 144
∴ (∝ + β)2 – 4∝β = 144
⇒ (– p)2 – 4 × 45 = 144 [Using (1)]
⇒ p2 – 180 = 144
⇒ p2 = 144 + 180 = 324
Thus, the value of p is ± 18.