In parallelogram ABCD , diagonals AC⎯⎯⎯⎯⎯ and BD⎯⎯⎯⎯⎯ intersect at point E, BE=2x2−3x , and DE=x2+10 .
What is BD ?
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units
The diagonals of a parallelogram bisect each other....therefore
2x^2 -3x = x^2 + 10 simplify
x^2 - 3x - 10 = 0 factor
(x -5)(x + 2) = 0
Setting each linear factor to 0 and solving for x....we have two possibilities, x = 5 or x = - 2
If x = 5, BD = 2 [ (5)^2 + 10 ] = 70
If x = -2, BD = 2 [ (-2)^2 + 10 ] = 28