Multiple choice

Find the value of P for which the following equation has equal roots $\displaystyle { px }^{ 2 }-8x+2p=0$

  1. $\displaystyle \pm 2\sqrt { 2 } $
  2. $\displaystyle \pm \sqrt { 2 } $
  3. $\displaystyle \pm \sqrt { 3 } $
  4. $\displaystyle \pm 2\sqrt { 3 } $
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A Correct answer
Explanation

For equal roots, the discriminant b^2 - 4ac must be 0. Here, (-8)^2 - 4(p)(2p) = 0 => 64 - 8p^2 = 0 => p^2 = 8 => p = +/- 2*sqrt(2).

AI explanation

For the equation px^2 - 8x + 2p = 0 to have equal roots, its discriminant must equal zero. Using the discriminant formula of D = b^2 - 4ac, we calculate (-8)^2 - 4(p)(2p) = 0. Solving 64 - 8p^2 = 0 gives p^2 = 8, so the value of P is plus or minus 2 times the square root of 2.

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