Question

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

Answer 1

Option b.

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√(-20)} {4}`

remember that

`i=√(-1)`

so

`x=\frac{-2\pmi√(20)} {4}`

`x=\frac{-2\pm2i√(5)} {4}`

simplify

`x=\frac{-1\pm i√(5)i} {2}`

therefore

In factored form the quadratic equation is equal to

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