Question 1184310
Find the value of p for which the equation (1-2p)x^2 + 8px - (2+8p) = 0 has two equal roots.
<pre>For equal roots to occur, the discriminant (b<sup>2</sup> - 4ac) of the equation MUST EQUAL 0.

With {{{matrix(3,3, a, "=", 1 - 2p, b, "=", 8p, c, "=", - 2 - 8p)}}}, we get: {{{matrix(6,3, b^2 - 4ac, "=", 0,
(8p)^2 - 4(1 - 2p)(- 2 - 8p), "=", 0,
64p^2 - 4(- 2 - 8p + 4p + 16p^2), "=", 0,
64p^2 - 4(- 2 - 4p + 16p^2), "=", 0,
64p^2 + 8 + 16p - 64p^2, "=", 0,
16p, "=", - 8)}}}
                                      {{{highlight_green(matrix(1,5, p, "=", (- 8)/16, "=", - 1/2))}}}</pre>