Solve the inequality 5x-1+-3x^2%0

{-3x^2+5x-1}\geq {0}

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Answer

$1.4343\geq x\geq 0.2324$

Step by step solution

Problem

${-3x^2+5x-1}\geq {0}$
1

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where $a=-3$, $b=5$ and $c=-1$

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

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

$x=\frac{5\left(-1\right)\pm \sqrt{5^2-1\left(-3\right)\left(-4\right)}}{-3\cdot 2}$
3

Multiply $-1$ times $5$

$x=\frac{-5\pm \sqrt{5^2-12}}{-6}$
4

Calculate the power

$x=\frac{-5\pm \sqrt{25-12}}{-6}$
5

Add the values $25$ and $-12$

$x=\frac{-5\pm \sqrt{13}}{-6}$
6

Calculate the power

$x=\frac{-5\pm \sqrt{12}}{-6}$
7

To obtain the two solutions, divide the equation in two equations, one when $\pm$ is positive ($+$), and another when $\pm$ is negative ($-$)

$x_1=\frac{-5+ \sqrt{12}}{-6}\:\:,\:\:x_2=\frac{-5- \sqrt{12}}{-6}$
8

Simplifying

$x_1=0.2324,\:x_2=1.4343$
9

Applying the quadratic formula we obtained the two solutions $x_1$ and $x_2$, with which we write the solution interval

$1.4343\geq x\geq 0.2324$

Answer

$1.4343\geq x\geq 0.2324$

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Problem Analysis

Main topic:

Quadratic formula

Time to solve it:

0.19 seconds

Views:

186