Question

Which two values of x are roots of the polynomial below? x2 + 5x+7

Answer 1

Answer:

The roots are

$x=\frac{-5+i\sqrt{3}}{2}$  and  $x=\frac{-5-i\sqrt{3}}{2}$

Step-by-step explanation:

we have

$x^{2} +5x+7$

To find the roots equate the polynomial to zero and cmplete the square

$x^{2} +5x+7=0$

$x^{2} +5x=-7$

$(x^{2} +5x+2.5^{2})=-7+2.5^{2}$

$(x^{2} +5x+6.25)=-0.75$

rewrite as perfect squares

$(x+2.5)^{2}=-0.75$

take square root both sides

$(x+2.5)=(+/-)\sqrt{-\frac{3}{4}}$

Remember that

$i=\sqrt{-1}$

substitute

$(x+2.5)=(+/-)i\sqrt{\frac{3}{4}}$

$(x+\frac{5}{2})=(+/-)i\frac{\sqrt{3}}{2}$

$x=-\frac{5}{2}(+/-)i\frac{\sqrt{3}}{2}$

therefore

The roots are

$x=\frac{-5+i\sqrt{3}}{2}$

$x=\frac{-5-i\sqrt{3}}{2}$