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Using the quadratic formula, solve the quadratic equation: $x-31 / x=0$
ago in Mathematics by Diamond (78,880 points) | 4 views

1 Answer

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To solve the equation, first we need to arrange it to appear in the form ax2 + bx $+c=0$ by removing the denominator:
$\mathrm{x}-31 / \mathrm{x}=0 \ldots$ First, we enlarge the equation by $\mathrm{x}$ :
$x^{\star} x-31 * x / x=0$
The quadratic formula to find the roots of a quadratic equation is:
$\mathrm{x}_{1,2}=(-\mathrm{b} \pm \sqrt{\Delta}) / 2 \mathrm{a}$ where $\Delta=\mathrm{b}^{2}-4 \mathrm{ac}$ and is called the discriminant of the quadratic equation.
In our question, the equation is $x^{2}-31=0$. By remembering the form $a x^{2}+b x+c=0$ :
$a=1, b=0, c=-31$
So, we can find the discriminant first, and then the roots of the equation:
$\Delta=b^{2}-4 a c=02-4 * 1 *(-31)=124$
$x_{1,2}=(-b \pm \sqrt{\Delta}) / 2 a=(\pm \sqrt{124}) / 2=(\pm \sqrt{4} \star 31) / 2$
$=(\pm 2 \sqrt{3} 1) / 2 \ldots$ Simplifying by 2 :
$x_{1,2}=\pm \sqrt{3} 1 \ldots$ This means that the roots are $\sqrt{31}$ and $-\sqrt{31}$.
ago by Diamond (78,880 points)

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