Question

Determine the number and type of solutions for x2 + 9x + 7 = 0.

1 Rational Double
2 Irrational
2 Rational
2 Complex

Answer 1

Can you find the discriminant?
For a quadratic equation \(ax^2+by+c\), the discriminant is \(b^2-4ac\)

Answer 2

yes the discriminant is 53

Answer 3

What would be the interpretation if the discriminant is >0 and real, retriceing a,b, & c are real?

Answer 4

* assuming

Answer 5

2 real roots?

Answer 6

exactly! Good work! :)

Answer 7

I'm not sure about rational and irrational thou?

Answer 8

If the discriminant is a perfect square you will get two rational roots.
If the discriminant is not a perfect square you will get two irrational roots.

Answer 9

so 53 isn't so it's option B

Answer 10

A rational number is a number that can be represented by a fraction of integers.
An irrational number is a number that result from square root of non-perfect squares.

Answer 11

Since the solution involves \(\sqrt{53}\), the solution will be irrational.
On the other hand, as @aum said, if the discriminant is a perfect square, then the solution is rational.

Answer 12

thank you to both of you!!! :) This one is C I believe

If an equation has a positive discriminant, how many times will the graph touch the x-axis?

zero
1
2
3

Answer 13

For
\(ax^2+bx+c=0\)
the solution is
\(\huge \frac{-b\pm \sqrt{b^2-4ac}}{2a}\)
so if the discriminant is irrational, the solution is irrational as well.

Answer 14

oh I see

Answer 15

C is correct, can you explain why?

Answer 16

I used an example of one of my previous problems. That problem too had two solutions

Answer 17

Correction to previous post:
if the discriminant is not a perfect square, the solution will be irrational.
I suppose you caught that! :)

Answer 18

:)

Answer 19

Here the discriminant is positive, so the solution is
\(\huge \frac{-b\pm something}{2a}\)
so that makes two distinct roots, hence crosses the x-axis twice.

Answer 20

yay so I was right! :)

Answer 21

I will post another in another post.