Question

Identify the zeros of the function f(x)=2x^2-4x+5 using the quadratic formula.

a. 1 +/-
`i(√(6) )/(2)`
b. 1 +/-
`i√(6)`
c. -1 +/-
`i√(6)`
d. 2 +/-
`(√(6) )/(2)`

Answer 1

A

Explanation:

Given the quadratic function

`f(x)=2x^2-4x+5`

In this function expression,

`a=2\\ \\b=-4\\ \\c=5`

Find the discriminant

`D=b^2-4ac=(-4)^2-4\cdot 2\cdot 5=16-40=-24`

Note that

`-1=i^2,`

then

`D=-24=24i^2\\ \\√(D)=√(24i^2)=2√(6)i`

Therefore,

`x_1=(-b-√(D))/(2a)=(-(-4)-2√(6)i)/(2\cdot 2)=(4-2√(6)i)/(4)=1-(√(6))/(2)i\\ \\x_2=(-b+√(D))/(2a)=(-(-4)+2√(6)i)/(2\cdot 2)=(4+2√(6)i)/(4)=1+(√(6))/(2)i`