What are the x-intercepts of the function f(x) = –2x2 – 3x + 20?

The X-intercepts are where the function = 0
factor the polynomial.

a*c factors that add to give b.
-2*20 = -40
-40 = -8*5

0 = -2x^2 - 8x + 5x + 20
0 = -2x(x + 4) + 5(x + 4)
0 = (-2x + 5)(x + 4)

anything multiplied by zero gives zero so one or both parenthesis have to be zero.

0 = x + 4
-4 = x
intercept (-4, 0)

0 = -2x + 5
-5 = -2x
5/2 = x
intercept ( 5/2, 0)

Let f(x)=0,
we get ,

so the answer(s) is(are) 2.5 and -4.
sorry if i make grammar mistakes.