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Step-by-step Solution

Solve the inequality $3x^2+7x+2\geq 0$

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Answer

$-2\geq x\geq -0.3333$

Step-by-step explanation

Problem to solve:

$3x^2+7x+2\geq 0$
1

To find the roots of a polynomial of the form $ax^2+bx+c$ we use the quadratic formula, where $a=3$, $b=7$ and $c=2$

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

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

$x=\frac{-1\cdot 7\pm \sqrt{7^2-4\cdot 3\cdot 2}}{2\cdot 3}$

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Answer

$-2\geq x\geq -0.3333$
$3x^2+7x+2\geq 0$

Main topic:

Inequalities

Time to solve it:

~ 0.4 seconds

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