Asked by Jane
Find all x such that x^2+5x<6. Express your answer in interval notation.
Thank you!
Thank you!
Answers
Answered by
Steve
x^2+5x-6 < 0
(x+6)(x-1) < 0
you know that the parabola opens upward, and that it crosses the x-axis at x = -6 and x=1. So
x^2+5x-6 < 0 in the interval (-6,1)
or, brute-forcing it,
if x>1, both factors are positive
if x < -6, both factors are negative.
in (-6,1) one is positive and the other negative
(x+6)(x-1) < 0
you know that the parabola opens upward, and that it crosses the x-axis at x = -6 and x=1. So
x^2+5x-6 < 0 in the interval (-6,1)
or, brute-forcing it,
if x>1, both factors are positive
if x < -6, both factors are negative.
in (-6,1) one is positive and the other negative
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