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Identify the zeros of the function f(x)=2x²-2x+13......how do I solve this?

1 Answer

5 votes

Answer:


x=0.5(+/-)2.5i

Explanation:

we know that

The zeros of he function or x-intercepts are the values of x when the function is equal to zero

so

For f(x)=0

we have


2x^(2) -2x+13=0

The formula to solve a quadratic equation of the form


ax^(2) +bx+c=0

is equal to


x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}

in this problem we have


2x^(2) -2x+13=0

so


a=2\\b=-2\\c=13

substitute in the formula


x=\frac{-(-2)(+/-)\sqrt{-2^(2)-4(2)(13)}} {2(2)}


x=\frac{2(+/-)√(-100)} {4}

Remember that


i=√(-1)

so


x=\frac{2(+/-)10i} {4}


x=0.5(+/-)2.5i

The function has no real solutions (complex solutions)

That means, the function do not intersect the x-axis

User Atlasmaybe
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