Question

1)A discriminant of –17 indicates what type of roots?


A)Two Irrational
B)Two Complex
C)Two Rational
D)One Rational Double

2)The quadratic 2x2 + 6x + 3 has what type of roots?


A)Two Complex
B)Two Rational
C)One Rational Double
D)Two Irrational

3)The quadratic x2 + 20x + 100 has what type of roots?
A)Two Complex
B)One Rational Double
C)Two Rational
D)Two Irrational

Answer 1

\[ For: y = ax^{2} + bx + c; Discriminant: b^{2} - 4ac \]
The rule of the discriminant is:
- For a positive discriminant, there are two real roots.
- For a zero discriminant, there is one real root.
- For a negative discriminant, there are two complex roots.

You should be able to use the discriminant in the last two questions just by plugging in the values for a,b,and c and figuring it out. The rules should answer the first question alone. :)

Answer 2

I still don't quiet understand this

Answer 3

* If you're trying to tell if its rational roots, you want a discriminant that is also a square number so it comes out nicely.

Answer 4

comes out nicely in the square-root on the quadratic formula, rather...

Answer 5

\[
\begin{split}
y=2x^{2} + 6x + 3\\
Discriminant:\\
6^{2} - 4*2*3 &= 36 - 24\\
&= 12\\
\end{split}
\]

12 is not a perfect square, but it is positive. So, we would have two irrational roots.

Answer 6

Hmm..
what exactly are you unsure about? Why they are rational/irrational?

Answer 7

The answers

Answer 8

Ahh.. well, alright then.
#1 is B (above)
#2 is C (above)

#3 is B
b^2 - 4ac => 20^2 - 4(1)(100)
= 400 - 400
= 0

This would be the 'rational double,' since in the quadratic equation you add and subtract this value to find the roots, and the value does not change when you add or subtract 0.

Answer 9

err, by quadratic equation, i mean the quadratic formula...