SOLUTION: Find the discriminant for each equation. Describe the roots. Give D, then the number of rational, irrational or complex roots. ( ex: 36, 2 rational) x^2 -16x +4 =0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find the discriminant for each equation. Describe the roots. Give D, then the number of rational, irrational or complex roots. ( ex: 36, 2 rational) x^2 -16x +4 =0      Log On


   

Question 627756: Find the discriminant for each equation. Describe the roots.
Give D, then the number of rational, irrational or complex roots. ( ex: 36, 2 rational)
x^2 -16x +4 =0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
From x%5E2-16x%2B4 we can see that a=1, b=-16, and c=4


D=b%5E2-4ac Start with the discriminant formula.


D=%28-16%29%5E2-4%281%29%284%29 Plug in a=1, b=-16, and c=4


D=256-4%281%29%284%29 Square -16 to get 256


D=256-16 Multiply 4%281%29%284%29 to get %284%29%284%29=16


D=240 Subtract 16 from 256 to get 240


So the discriminant is D=240


Since the discriminant is greater than zero, this means that there are two real solutions.


Since 240 is NOT a perfect square, these two real solutions are irrational solutions.


So we have 2 real and irrational solutions.

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