Mathematics: What are the roots of 2x^2+4x+7? Use the quadratic formula. Show your work

1. First a reflection in the y-axis. Then a translation upwards of 7 units.2. First a translation upwards of 7 units Then a reflection in the y axis....

What are the roots of 2x^2+4x+7? Use the quadratic

Ответ:

aidanfbussiness

18.01.2022

Mathematics

The roots are

$x=-1+i\frac{\sqrt{10}}{2}$

$x=-1-i\frac{\sqrt{10}}{2}$

Step-by-step explanation:

we have

2x^2+4x+7

To find the roots equate the equation to zero

2x^2+4x+7=0

we know that

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

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

in this problem we have

2x^2+4x+7=0

$a=2\\b=4\\c=7$

substitute in the formula

$x=\frac{-4\pm\sqrt{4^{2}-4(2)(7)}} {2(2)}$

$x=\frac{-4\pm\sqrt{-40}} {4}$

Remember that

$i=\sqrt{-1}$

$x=\frac{-4\pmi\sqrt{40}} {4}$

$x=\frac{-4\pm2i\sqrt{10}} {4}$

simplify

$x=\frac{-2\pm i\sqrt{10}} {2}$

therefore

The roots are

$x=\frac{-2+i\sqrt{10}} {2}=-1+i\frac{\sqrt{10}}{2}$

$x=\frac{-2-i\sqrt{10}} {2}=-1-i\frac{\sqrt{10}}{2}$

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What are the roots of 2x^2+4x+7? Use the quadratic formula. Show your work

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