SOLUTION: Solve (x-1)(x+4)<0

Question 620182: Solve (x-1)(x+4)<0
Answer by fcabanski(1391) (Show Source): You can put this solution on YOUR website!
(x-1)(x+4)<0 | Change < to = and find the zeroes by solving for x (each factor).

x=1, x=-4 |Set up and test intervals based on those zeroes: x < -4, -4 < x < 1, x > 1

x < -4, choose -4: (-5-1)(-5+4) = -6*-1 = 6 which is not < 0. This interval doesn't work.

-4 < x < 1, choose 0: (0-1)(0+4) = -1*4 = -4 < 0. This interval works.

x >1, choose 2: (2-1)(2+4) = 1*6 = 6 not < 0. This interval doesn't work.

The answer is -4 < x < 1.

If you know parabolas, or graph this, you will see this is less than 0 between the zeroes. Check out the graph (at the bottom).

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=25 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 1, -4. Here's your graph:

Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.)

RELATED QUESTIONS
Solve.... (answered by edjones)

1.solve (2x - 3)(x - 4) =... (answered by stanbon)

solve:... (answered by solver91311)

solve {{{ (x+4)(x-1)/(x+3)>0 }}} (answered by Fombitz)

solve 2^x-4^(1/(2+x))+8^x =... (answered by Vladdroid)

Solve each matrix equation for X 1 0 0 0 1 0 0 0 1 X = 4 -5... (answered by jim_thompson5910)

Solve for x:... (answered by richwmiller)

Solve: 16^(x) + 4^(x+1) - 3 = 0... (answered by jim_thompson5910)

solve for x, [-5 0 -1] [2 1 0] = 4 [x 3... (answered by robertb)