Question

Calculate the discriminant.

x2 – 2x + 4 = 0

A.
12

B.
–12

C.
20

D.
0

Answer 1

the discriminant for a quadratic

\[ax^2 + bx + c = 0\]

is

\[x = b^2 - 4 \times a \times c\]

in the question a = 1, b = -2 and c = 4

so substitute and calculate the answer....

take care with squaring the negative

Answer 2

It might be more appropriate to use a different variable than x for the exact discriminant. Usually I see capital delta, but any old letter (d, D, etc.) would be fine: \(\color{blue}\Delta = b^2 - 4ac\)

Since its motivation for quadratic equations stems from the quadratic formula:
\( x = \dfrac{-b \pm \sqrt{\color{blue}{b^2 - 4ac}}}{2a} \qquad = \dfrac{-b \pm \sqrt{\color{blue}{\Delta}}}{2a}\)
But regardless, calculating \( b^2 - 4ac \) from the equation is our goal. :)