In parallelogram abcd , diagonals ac and bd intersect at point e, ae=2x2−3x , and ce=x2+4 . what is ac ?

Given that ABCD is a parallelogram.

And diagonals AC and BD intersect at E point.

Therefore, AE = CE , because the diagonals of a parallelogram bisect each other.

Given AE=2x^2−3x , and CE=x^2+4.

Putting them equal.

Factoring quadratic

(x-4)(x+1)=0

.

We can't take a negative value.

Therefore plugging x=4 in AE=2x^2−3x, we get

AE = 2(4)^2 - 3(4) = 32 - 12 = 20.

AC= 2 × 20 = 40.