Question

Find the discriminant of the related quadratic function and determine the number of real and imaginary solutions of 2y^2 - 4y + 1 = 0.

Answer 1

Equation: \[2y ^{2} - 4y + 1 = 0\]

Answer 2

the discriminant for a quadratic

\[ay^2 + by + c = 0\]

can be found using

\[\Delta = b^2 - 4ac\]

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

just substitute and calculate an answer

Answer 3

and you may like to ask your teacher, what the question asks how many solutions...

and suggest to the teacher a degree 2 polynomial will have 2 solutions...

Answer 4

@campbell_st - The answer would be:
\[(-4)^{2} - 4(2)(1)\] which is equal to 8.

If the discriminant is greater than 0, then there are 2 real solutions, right?

Answer 5

http://www.regentsprep.org/regents/math/algtrig/ate3/discriminant.htm

Answer 6

conditions for the discriminant

discriminant > 0 2 real unequal solutions is discriminant is a perfect square the solutions are rational, otherwise the solutions will be real and irrational.

discriminant = 0 2 real equal solutions

discriminant < 0 2 complex solutions.

Answer 7

yes the solutions are unequal and real... do look at 8... is it a square number..?

if so the solutions are real, unequal and rational.

if not, real unequal and irrational

Answer 8

@campbell_st - Thank you so much!

Answer 9

glad to help