Question

Identify the zeros of the function f(x) = 4x2 − 8x − 1 using the Quadratic Formula. HELP ASAP!!

Answer 1

`1+(√(5))/(2),1-(√(5))/(2)`

Explanation:

The given equation is
`4x^(2)-8x-1`

Let
`a` be the coefficient of
`x^(2)`

Let
`b` be the coefficient of
`x`

Let
`c` be the constant.

Then the roots α,β for the equation
`ax^(2)+bx+c` are
`\frac{-b+\sqrt{b^(2)-4ac} }{2a},\frac{-b-\sqrt{b^(2)-4ac} }{2a}`

So,α=
`\frac{-b+\sqrt{b^(2)-4ac} }{2a}=(8+√(64+16) )/(8)=(8+4√(5))/(8)=1+(√(5))/(2)`

β=
`\frac{-b-\sqrt{b^(2)-4ac} }{2a}=(8-√(64+16) )/(8)=(8-4√(5))/(8)=1-(√(5))/(2)`.

So the roots are
`1+(√(5))/(2),1+(√(5))/(2)`