How do you solve $13x^2-5x<=0$ ?

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Answer 1 · 2016-08-12T15:47:45

Solve as a regular quadratic and then select test points.

$13x^2 - 5x = 0$

$x(13x - 5) = 0$

$x = 0 and 5/13$

$color(blue)("Test point 1"-> "-1")$

$13(-1)^2 - 5(-1) ≤^? 0$

$18≤^O/ 0$

This inequality is obviously not true, so let's go on to test point $2$ .

$color(red)("Test point 2" -> "1/4"$

$13(1/4)^2 - 5(1/4) <=^? 0$

$-0.4375 <= 0$

Hence, the interval that is the solution to this inequality $0<= x <= 5/13$ .

On a number line, the solution would be the turquoise rectangle.

enter image source here

Hopefully this helps!

How do you solve 13x^2-5x<=013x^2-5x<=0?