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Step-by-step Solution

Solve the inequality $1-x-2x^2\geq 0$

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Answer

$0.5\geq x\geq -1$

Step-by-step explanation

Problem to solve:

$1-x-2x^2\geq 0$
1

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

$x=\frac{-1\cdot -1\pm \sqrt{{\left(-1\right)}^2+8}}{2\cdot -2}$

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Answer

$0.5\geq x\geq -1$
$1-x-2x^2\geq 0$

Main topic:

Inequalities

Time to solve it:

~ 0.41 seconds

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