Q12 of 227 Page 114

If α and β are roots of 5x2 – px + 1 = 0 and α – β = 1, then find P.

Roots of any quadratic equation are α and β


By comparing the given equation with ax2 + bx + c = 0


a = 5, b = –p and c = 1






α – β = 1


α – β = (α + β)2 – 4αβ



⇒


⇒


⇒ p2 – 20 = 25


⇒ p2 = 25 + 20


⇒ p2 = 45


⇒ p = √45


⇒ p = 3√5


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