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Step-by-step Solution

Solve the inequality $19x^2-140x+241>0$

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Answer

$2.7412>x>4.6272$

Step-by-step explanation

Problem to solve:

$19x^2-140x+241>0$
1

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where $a=19$, $b=-140$ and $c=241$

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

Substituting the values of the coefficients of the equation in the quadratic formula

$x=\frac{-1\cdot -140\pm \sqrt{{\left(-140\right)}^2-4\cdot 19\cdot 241}}{2\cdot 19}$

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Answer

$2.7412>x>4.6272$
$19x^2-140x+241>0$

Main topic:

Inequalities

Time to solve it:

~ 0.36 seconds