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Step-by-step Solution

Solve the inequality (x+2)(x-5)<0

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Answer

$-2<x<5$

Step-by-step explanation

Problem to solve:

$\left(x+2\right)\left(x-5\right)<0$
1

The product of two binomials of the form $(x+a)(x+b)$ is equal to the product of the first terms of the binomials, plus the algebraic sum of the second terms by the common term of the binomials, plus the product of the second terms of the binomials. In other words: $(x+a)(x+b)=x^2+(a+b)x+ab$

$x^2-3x-10<0$
2

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where $a=1$, $b=-3$ and $c=-10$

$x =\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

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Answer

$-2<x<5$
$\left(x+2\right)\left(x-5\right)<0$

Main topic:

Quadratic formula

Time to solve it:

~ 0.67 seconds