Question

using the discriminant find the NUMBER of solutions 2x^2-4x+1=0

Answer 1

Discriminant :
\[b^2 - 4ac\]

Answer 2

So:

Ax^2 + Bx + C = 0

2x^2-4x+1=0

a = 2
b = -4
c = 1

Answer 3

Therefore:

\[b^2 - 4ac\]
\[(-4)^2 - 4(2)(1)\]
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Answer 4

\[(-4)^2 - 4(2)(1)\]
\[16 - 8 \]
\[8\]

Answer 5

So:

If discriminant < 0 , then there exist 2 complex solutions


If discriminant = 0 , then there exist 1 repeated real solution


If discriminant > 0 , then there exist 2 distinct real solutions

Answer 6

Thank you!

Answer 7

so:

8 > 0

therefore:

If discriminant > 0 , then there exist 2 distinct real solutions