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Alecsey [184]
3 years ago
10

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

Mathematics
1 answer:
garik1379 [7]3 years ago
7 0

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}))  

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