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If the roots of the quadratic equation px(x − 2) + 6 = 0 are equal, find the value of p

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Given quadratic equation is px (x – 2) + 6 = 0 

⇒ px2 − 2px + 6 = 0 … (1)

By comparing equation (1)with ax2 + bx + c = 0, 

we get a = p, b = −2p and c = 6. 

Since given that the given quadratic equation has equal roots. 

∴ D = b2– 4ac = 0 (∵ for equal roots D = 0) 

⇒(−2p)2 − 4 × p × 6 = 0 

⇒ 4p2 − 24p = 0 

⇒ 4p (p – 6) = 0 

⇒ p = 0 or p – 6 = 0 

⇒ p = 0 or p = 6 but p ≠ 0 

(∵ If p = 0 then given equation is not quadratic equation) 

Hence the value of p is 6, for which the given quadratic equation have equal roots.

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