^{2} +px + 45 is equal to 144, find the value of p.

The given quadratic polynomial is *f*(*x*) = *x*^{2} + *px* + 45.

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)]

⇒ *p*^{2} – 180 = 144

⇒ *p*^{2} = 144 + 180 = 324

Thus, the value of *p* is ± 18.

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