Question

Write f(x) = 2x^2 + 2x + 3 in factored form.

Answer 1

Answer:

Option b.

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

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

s equal to

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

in this problem we have

$2x^{2} +2x+3=0$  

so

$a=2\\b=2\\c=3$

substitute in the formula

$x=\frac{-2\pm\sqrt{2^{2}-4(2)(3)}} {2(2)}$

$x=\frac{-2\pm\sqrt{-20}} {4}$

remember that

$i=\sqrt{-1}$

so

$x=\frac{-2\pmi\sqrt{20}} {4}$

$x=\frac{-2\pm2i\sqrt{5}} {4}$

simplify

$x=\frac{-1\pm i\sqrt{5}i} {2}$

therefore

In factored form the quadratic equation is equal to

$2x^{2} +2x+3=2(x-(\frac{-1+i\sqrt{5}} {2}))(x-(\frac{-1-i\sqrt{5}} {2}))$