(x-4)(x+9)>0?

Question

all i know is that this is a quadratic inequality inequality and we have to write the solution in interval notation

Answer 1

f (x) = (x - 4)(x + 9)
f (x) > 0 for x > 4
f (x) > 0 for x < - 9

Answer 2

Ö¶(x - 4)(x + 9) has two roots -9 and 4

If -9 <= x <=4:

x+9 >= -9 + 9 = 0
x - 4 <= 4 - 4 = 0

(x - 4)(x + 9) <= 0 Because it is a product of a non-negative and a non-positive numbers.

If x< -9 the x<4
x - 4 < 4 - 4 = 0
x + 9 < -9 + 9 = 0

(x - 4)(x + 9) > 0 Because it is a product of 2 negative numbers.

Likewise, if x>4, (x - 4)(x + 9) > 0 because it is a product of 2 positive numbers.

x should be in:
(-inf -9) U (4 inf)

Answer 3

Given two factors, (x - 4) and (x + 9), we know that the inequality will be true when both factors are > 0 or when both factors are < 0

x - 4 > 0
x > 4

x + 9 > 0
x > - 9

Both > 0 if x > 4

x - 4 < 0
x < 4

x + 9 < 0
x < - 9

Both < 0 if x < -9

x < - 9 or x > 4

Answer 4

For the equation to be true, neither of the parenthesis must be negative, or both need to be. Also, neither can equal zero.

The equation equals zero at +4 and -9.

For x equals a value greater than 4, the equation will be positive. Therefore, (4, inf) is the first portion.

For x equals a value less than -9, both quantities will be negative, resulting in a positive.

The domain is as follows.
(-inf, -9) U (4, inf)

Answer 5

well if (x-4) (x+9)>0 that means that neither (x-4) nor (x+9) can equal 0.
which means x-4 >0 and x+9 >0
x - 4 + 4 > 0 + 4
x > 4

AND
x + 9 > 0
x + 9 - 9 > 0 - 9
x > -9

That means (- 9, 4) U (4, infinite)

Hope this helps.

Answer 6

(x-4)(x+9)>0

thus (x-4)(x+9) = 0 when x = 4 or -9

if -9 < x < 4, (x-4)(x+9) < 0

but if x < -9 or > 4, (x-4)(x+9) > 0

thus x < -9 or x > 4

Answer 7

expand into x^2 + 5x -36 > 0
x^2 +5x>36


OR you can just do -9

Answer 8

+·+=+ or -·-= + -->

S={x in R / x < -9 or x>4} = (-inf, -9) U (4, inf)

= ]-inf, -9[ U ]4, inf[

Saludos.