i need help on a math problem?

Question

determine the interval in which the polynomial x^2-4x-5 is entirely negative

Answer 1

This is the equation of a parabola. Set it equal to zero, factor it, and solve:

x^2 - 4x - 5 = (x + 1)(x - 5) = 0 Thus x = -1 or x = 5, that is, the polynomial has value zero (it crosses the x-axis) when x = -1 and again when x = 5.

Now choose any value for x that is between -1 and 5, say x = 0, in order to see where its values are in the interval (-1,5). When x = 0, x^2 - 4x -5 = 0^2 - 4*0 -5 = 0 - 0 - 5 = -5 < 0, so the polynomial is negative between its two zeroes.

Now we know that the polynomial is negative on the interval (-1,5), that is, when -1 < x < 5

Answer 2

x^2-4x-5
x^2-4x-5 < 0 factor the ploynomial first
(x-5)(x+1) < 0

then take the factors separately

x-5 < 0
x < 5

x+1 > 0
x > -1
meaning -1 < x <5
meaning values are 0, 1, 2, 3, and 4 only

Answer 3

Graph the function.

Then, your answer would be in an inequality form. Say, for instance, that an equation is entirely negative from X being -4 to X being 2. The interval would be -4(less than or equal to)X(less than or equal to)2. As in, -4

Answer 4

what grade are you in because i am in 7th and we haven't learned that yet. Sorry.