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Let α,β be the zeroes of the given quadratic polynomial f(x)=x
2
+px+45
∴α+β=−p,αβ=45
It is given that, (α−β)
2
=144
⇒(α+β)
2
–4αβ=144
⇒(–p)
2
–4×45=144
⇒p
2
–180=144
⇒p
2
=144+180
⇒p
2
=324
⇒p=±
324
∴p=±18
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