Question

A quadratic equation is shown below:

9x2 − 16x + 60 = 0

Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work. (5 points)

Part B: Solve 4x2 + 8x − 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you chose the method used. (5 points)

Answer 1

dis ill figure out

Answer 2

thanks for your help

Answer 3

@benlindquist @hartnn any ideas?

Answer 4

the radicand or discriminant for \(ax^2+bx+c =0\)
is
\(b^2-4ac\)

can you find the a,b,c values first?

Answer 5

a=9 b=-16 and c=60

Answer 6

good!
so what is
\(b^2-4ac = (-16)^2 - 4\times9\times 60 = .. ?\)

Answer 7

-1904

Answer 8

yes.

so the discriminant came out to be negative.
Do you already know what that means ?

Answer 9

no..

Answer 10

If the discriminant is negative,
that means the roots of the quadratic equation are complex conjugate in nature.

Answer 11

In other words,
both of the roots are NOT real roots.

Answer 12

so does that mean that the equation has unapplicable answers

Answer 13

You can either mention :
A. 2 Complex conjugate solutions
or
B. 2 non-real solutions

both will be accepted.

Answer 14

it really depends on what (if) you have been already taught by your teacher.

Answer 15

ok thanks a lot. I already have something for part B but I just want to make sure I got it correct. Give me a minute to type it.

Answer 16

sure :)

Answer 17

yeah, think of it this way - numbers are not actually real. They aren't present in the real world. You can have 2 of something, but not 2 itself. While most would agree there are properties of things that can be modelled with such a "twoness", there you can't have "two". The same applies with complex numbers. The things that complex numbers wind up modelling, however, are different and generally not taught until at least your second year in college. For now, you can simply state that this equation has 2 complex solutions and that no real solutions exist... This is analogous to saying that you can't express a solution in rational numbers (common when you have a square root).

Answer 18

thx @inkyvoyd

Answer 19

@hartnn this is part b

First we factor 4x^2+8x-5=0
4x^2+10x-2x-5=0
2x(2x+5)-(2x+5)=0
(2x+5)(2x-1)=0
2x+5=0 or 2x-1=0
x= -2.5 x=0.5

Answer 20

very good work! :)
its correct.

\(\huge \checkmark \)

Answer 21

THank you so much for your help! :)

Answer 22

welcome ^_^