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Question
Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots: px2 – 4x + 3 = 0
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Solution
px2 – 4x + 3 = 0
Here a = p, b = -4, c = 3
∴ D = b2 - 4ac
= (-4)2 - 4 x p x 3
= 16 - 12p
∵ The roots are equal
∴ D = 0
⇒ b2 - 4ac = 0
⇒ 16 - 12p = 0
⇒ 12p = 16
⇒ p = `(16)/(12) = (4)/(3)`
∴ p = `(4)/(3)`.
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