Question

A quadratic equation is shown below:
3x2 - 16x + 2 = 0

Part A: Describe the solution(s) to the equation by just determining the discriminant. Show your work. (3 points)

Part B: Solve 9x2 + 3x - 2 = 0 by using an appropriate method. Show the steps of your work and explain why you chose the method used. (4 points)

Part C: Solve 3x2 - 10x + 2 = 0 by using a method different from the one you used in Part B. Show the steps of your work. (3 points)

Answer 1

Do you know what a discriminant is ?

Answer 2

no I dont

Answer 3

Have you ever used a quadratic formula ? If so, then you should be

familiar with this, \(\LARGE\color{black}{ x= \frac{-b±\sqrt{\color{blue}{b^2-4(a)(c)}}}{2a} }\) .


The discriminant is the blue part.

Answer 4

ohhhh yes I remember

Answer 5

you will know that if b²-4ac is equal to a negative number (when you plug your values in) then you have no (real) solutions.
IF your discriminant - the b²-4ac is a zero, then you will have 1 solution.

And if it is equal to some positive number (when you plug your a,b,c into it) then you get 2 soltuions.


(and if the discriminant, the b²+4ac is a perfect square, (such as 1, 4, 9, 16, 25, 36 and on ) then you can factor it )

Answer 6

\(\normalsize\color{black}{ \color{blue}{3}x^2 \color{green}{-16}x + \color{red}{3} = 0}\) Compare to \(\normalsize\color{black}{ \color{blue}{a}x^2 +\color{green}{b}x + \color{red}{c} = 0}\)

Answer 7

okay I will

Answer 8

Can you find the discriminant ? Tell me what you get

Answer 9

I don't tjhink im doing it right

Answer 10

you say that you don't think you are dong this right, but can I please see WHAT you are doing, to verify ?

Answer 11

Can you find what b² - 4ac is going to be equal to in YOUR case, or need help with that ?

Answer 12

(x+6)(x-3)?

Answer 13

You need to just find the discriminant. Don't solve it yet:)

Answer 14

\[10\pm \sqrt{(-10)^{2}}-4(3)(2)\]

Answer 15

2(3) on the bottom

Answer 16

Which equation are you doing? I was referring to the PART A, where you have 3x²-16x+2=0

And the discriminant is `(-16)² - 4(3)(2)`
`256 - 24`
`232`

Answer 17

ohh im sorry

Answer 18

so that was for part a?

Answer 19

you get that the discriminant is 232, and when the discriminant is positive you will have 2 solutions.

Answer 20

yupp

Answer 21

I got disconnected. Durn it !

Answer 22

its okay(:

Answer 23

\(\normalsize\color{black}{ 3x^2 - 10x + 2 = 0}\)

use the quadratic formula, because you can't factor since the discriminant is not a perfect square (but it is a 74), and completing the square isn't good, because you already starting with an odd coefficient in front of x².

Answer 24

\(\LARGE\color{black}{ x=\frac{-(-10)±\sqrt{(-10)^2-4(3)(2)}}{2(3)} }\) go for it.