Question

p2+p-(a+1)(a+2)........
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Answer 1

Given: The equation p^2 + p - ( a + 1 ) ( a + 2 ) = 0

To find: The roots of the given equation.

Solution:

• Now we have given the equation as:

                     p^2 + p - ( a + 1 ) ( a + 2 ) = 0

• Now we know the formula for roots of the equation as:

                     -b ± √D / 2a

• So applying it, we get:

                     -1 ± √((-1)^2 - 4 (-( a + 1 ) ( a + 2 ))) / 2

                     -1 ± √(1 + 4( a^2 + 2a + a + 2 ) / 2

                     -1 ± √(1 + 4( a^2 + 3a + 2 ) / 2

                     -1 ± √(1 + 4a^2 + 12a + 8 ) / 2

                     -1 ± √(4a^2 + 12a + 9 ) / 2

                     -1 ± √(2a + 3)^2 / 2

                     -1 ± (2a + 3) / 2

• Now there are two cases:

                     -1 + (2a + 3) / 2 and -1 - (2a + 3) / 2

                     2a + 2 / 2 and 2 - 2a / 2

                     a + 1 and 1 - a

Answer:

            So the roots of the given equation are a + 1 and 1 - a.