Name: Quadratic formula with irrational roots: solution walkthrough
Uploaded: 2026-11-13
Duration: 2 min 19 s
Description: What are the solutions of the equation 2x² - 4x - 1 = 0? Try it, then watch the animated solution.

The solutions are where the graph of

y = 2x^2 - 4x - 1

crosses the

x

-axis. It will not factor, so use the quadratic formula.

Match the equation with

ax^2 + bx + c = 0

: here

a = 2

,

b = {-4}

and

c = {-1}

. The signs belong to the numbers.

Under the root:

({-4})^2 - 4(2)({-1}) = 16 + 8 = 24

. Also

{-b} = 4

and

2a = 4

, so

x

is

4 \pm \sqrt{24}

, all over

4

.

Simplify:

\sqrt{24} = \sqrt{4 \cdot 6} = 2\sqrt{6}

. Then divide all three terms by

2

:

x

is

2 \pm \sqrt{6}

, all over

2

.

Check with the graph:

\sqrt{6} \approx 2.45

, so

x \approx 2.22

or

x \approx {-0.22}

. That is where the curve crosses.

Traps: using

b

for

{-b}

, getting

16 - 8

under the root, and dividing by

2

instead of

2a

.

Try it first