Question

Please help!!!! Ill give medals!!!!



9x^2 -16x+60=0

Part A: Describe the solution(s) to the equation by just determining the discriminant.

Part B: Solve 4x^2+8x-5=0 by using an appropriate method. Show the steps of your work and explain why you chose the method used.

Part C:Solve 2x^2-12x+5=0 by using the one in part B.

Answer 1

Are you familiar with the form \[\Delta = b^2 -4ac\]?
That is the discriminant of the Quadratic form \[ax^2 + bx + c\]

Answer 2

whats the triangle for

Answer 3

Delta, stands for discriminant in this case

Answer 4

So, we need the first equation:
Substitute values for a, b and c
And then we can go head and interpret the equation, and what it tells us about the nature of the roots

Answer 5

Are you with me?

Answer 6

yes so what do we need to substitute with a, b, and c

Answer 7

The coefficients of the quadratic equation\[9x^2-16x +60 \rightarrow a = 9, b=-16, c =60\]

Answer 8

oh ok

Answer 9

ax^2-bx+c like this?

Answer 10

Subst into this: \[\Delta = b^2 -4ac\]

Answer 11

whats with the triangle

Answer 12

Just evaluate the expression on the right with those values, I'll explain once you have you've done so...

Answer 13

\[\Delta=-16x^2-(4*9*60)\]

Answer 14

didn't mean to put the parenthesis

Answer 15

No, our discriminant eqn doesn't contain x^2. What we have is something like this\[\Delta = b^2 - 4ac \rightarrow (-16)^2 - 4*9*60 = 216 - 2160 \rightarrow \Delta = -1944\]

Answer 16

oh ok

Answer 17

Now this is how we interpret the value of Δ:

If the value is > 0, there are 2 different real roots
If the value is 0, there are two real equal roots
If the value is < 0, there are two different complex roots

Now, we wound up with a value of -1944, which is less than 0; and this tells us that there two different complex roots to our given polynomial

Answer 18

i get it. So Is that it for part A?

Answer 19

Yep, pretty much

Answer 20

Part B wants to test your knowledge on solving these kind of equation. Just how many methods can you employ in solving them?

Answer 21

um would factoring it be a method?

Answer 22

yeah, that's one

Answer 23

I really don't have much time left, but here is what I think:

Factoring would require you to have two factors that when multiplied give you coeff of x^2 times constant, c, and then when added give coeff of x.

Clearly -20 and 8 don't have two of these common factors, so factoring is not a way to go to solve this solution

Answer 24

oh ok then what about using the quadratic formula

Answer 25

Good, that would be a better option, or completing the square still... :)

Answer 26

So, if you chose the Quadratic formula, then you'd be using it for Part C too. I hope I've cleared up much of the confusion here ...