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Using the quadratic formula, solve the quadratic equation: $x^{2}-9 x+14=0$
ago in Mathematics by Diamond (78,880 points) | 5 views

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To solve the equation, we need the equation in the form $a x^{2}+b x+c=0$. $x^{2}-9 x+14=0$ is already in this form.
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 $x^{2}-9 x+14=0$. By remembering the form $a x^{2}+b x+c=0$ :
$\mathrm{a}=1, \mathrm{~b}=-9, \mathrm{c}=14$
So, we can find the discriminant first, and then the roots of the equation:
$\Delta=b^{2}-4 a c=(-9)^{2}-4 * 1 * 14=81-56=25$
$x_{1,2}=(-b \pm \sqrt{\Delta}) / 2 a=(-(-9) \pm \sqrt{25}) / 2=(9 \pm 5) / 2$
This means that the roots are, $x_{1}=(9-5) / 2=2$ and $x^{2}=(9+5) / 2=7$
ago by Diamond (78,880 points)

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