Question

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

Answer 1

$1+\dfrac{\sqrt{5}}{2},1-\dfrac{\sqrt{5}}{2}$

Step-by-step 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 $\dfrac{-b+\sqrt{b^{2}-4ac} }{2a},\dfrac{-b-\sqrt{b^{2}-4ac} }{2a}$

So,α=$\frac{-b+\sqrt{b^{2}-4ac} }{2a}=\frac{8+\sqrt{64+16} }{8}=\frac{8+4\sqrt{5}}{8}=1+\frac{\sqrt{5}}{2}$

β=$\frac{-b-\sqrt{b^{2}-4ac} }{2a}=\frac{8-\sqrt{64+16} }{8}=\frac{8-4\sqrt{5}}{8}=1-\frac{\sqrt{5}}{2}$.

So the roots are $1+\frac{\sqrt{5}}{2},1+\frac{\sqrt{5}}{2}$