Given 5n² + 6n + 7 = n² - 4n :

a. Find the value of the discriminant.

b. State the number and type of roots/solutions/zeros.[2 real, 2 imaginary, 1 real]

Question

Given 5n² + 6n + 7 = n² - 4n :

a. Find the value of the discriminant.

b. State the number and type of roots/solutions/zeros.[2 real, 2 imaginary, 1 real]

nory · Answer

First: Get all the terms on one side, and a 0 on the other.

anonymous · Answer

4n^2+10n+7=0

anonymous · Answer

@Nory

nory · Answer

Good. Now remember the discriminant formula:
$$\sqrt{b ^{2}-4ac}$$

nory · Answer

Oops...I didn't need the square root there.

nory · Answer

Anyway, if the bit under the square root is positive, then it has two real solutions. If it is 0, then it has one real solution, and if it is negative, no real solutions.

nory · Answer

So figure out what a, b, and c are and plug them into the formula.

anonymous · Answer

would i use the quadratic formula

nory · Answer

That's the second step, the step where you actually _find_ the solutions.
See, do you see the expression I wrote? The one with the square root? Does that look familiar? It's actually part of the quadratic formula.

anonymous · Answer

4n^2+10n+7=0

10^2-4(10)(7)
100-40(7)

100-280

-180

anonymous · Answer

its that about right?

nory · Answer

Just about. You just missed one step. When you do b^ - 4ac, the second term should be 4(4)(7) instead of 4(10)(7). But I see you have the basic idea.

anonymous · Answer

so this has 2 solutions ? and the value is 12?

nory · Answer

Well, the discriminant would be
10^2 - 4(4)(7)
100 - 16*7
And (you can use a calculator):
100 - 112
-12

nory · Answer

The discriminant is negative, so what does that tell you about the solutions?

anonymous · Answer

theres no real solution

nory · Answer

exactly. Good job. So therefore, there are 2 imaginary solutions. And you're done!

nory · Answer

good work. :)