If the squared difference of x^2+px+45 is 144. Find p.urgent brainlist.
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Let α,β are the roots of the quadratic polynomial f(x) = x2+px+45 then
α + β = -p ---------(1) and αβ = 45
Given (α - β)2 = 144
∴ (α + β)2 – 4αβ = 144
⇒ (– p)2 – 4 × 45 = 144 [Using (1)]
⇒ p 2 – 180 = 144
⇒ p 2 = 144 + 180 = 324
Thus, the value of p is ± 18.
α + β = -p ---------(1) and αβ = 45
Given (α - β)2 = 144
∴ (α + β)2 – 4αβ = 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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